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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=150" class="pagination-link " aria-label="Page 4" aria-current="page">4 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=200" class="pagination-link " aria-label="Page 5" aria-current="page">5 </a> </li> <li><span class="pagination-ellipsis">…</span></li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.15467">arXiv:2501.15467</a> <span> [<a href="https://arxiv.org/pdf/2501.15467">pdf</a>, <a href="https://arxiv.org/format/2501.15467">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Bipartite expansion beyond biparticity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Anokhina%2C+A">A. Anokhina</a>, <a href="/search/hep-th?searchtype=author&query=Lanina%2C+E">E. Lanina</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2501.15467v1-abstract-short" style="display: inline;"> The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary $N$, i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provides a generic and straightforward non-perturbative calculus in an arbitrary Chern--Simons theory. Technically, this approach is restricted to knots and links which possess bipartite realizations, i.e. can be entirely glu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15467v1-abstract-full').style.display = 'inline'; document.getElementById('2501.15467v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.15467v1-abstract-full" style="display: none;"> The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary $N$, i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provides a generic and straightforward non-perturbative calculus in an arbitrary Chern--Simons theory. Technically, this approach is restricted to knots and links which possess bipartite realizations, i.e. can be entirely glued from antiparallel lock (two-vertex) tangles rather than single-vertex $R$-matrices. However, we demonstrate that the resulting positive decomposition (PD), i.e. the representation of the fundamental HOMFLY polynomials as positive integer polynomials of the three parameters $蠁$, $\bar蠁$ and $D$, exists for arbitrary knots, not only bipartite ones. This poses new questions about the true significance of bipartite expansion, which appears to make sense far beyond its original scope, and its generalizations to higher representations. We have provided two explanations for the existence of the PD for non-bipartite knots. An interesting option is to resolve a particular bipartite vertex in a not-fully-bipartite diagram and reduce the HOMFLY polynomial to a linear combination of those for smaller diagrams. If the resulting diagrams correspond to bipartite links, this option provides a PD even to an initially non-bipartite knot. Another possibility for a non-bipartite knot is to have a bipartite clone with the same HOMFLY polynomial providing this PD. We also suggest a promising criterium for the existence of a bipartite realization behind a given PD, which is based on the study of the precursor Jones polynomials. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.15467v1-abstract-full').style.display = 'none'; document.getElementById('2501.15467v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">37 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2501.14714">arXiv:2501.14714</a> <span> [<a href="https://arxiv.org/pdf/2501.14714">pdf</a>, <a href="https://arxiv.org/ps/2501.14714">ps</a>, <a href="https://arxiv.org/format/2501.14714">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Super-Hamiltonians for super-Macdonald polynomials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2501.14714v1-abstract-short" style="display: inline;"> The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables $p_k$ new Grassmann time variables $胃_k$ are introduced, and the Hamiltonian is represented as a differential operator acting on a space of functions of both types of variables $p_k$ and $胃_k$. Eigenfunctions for this Hamiltonian are a suitable generalization of Macdonal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.14714v1-abstract-full').style.display = 'inline'; document.getElementById('2501.14714v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.14714v1-abstract-full" style="display: none;"> The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables $p_k$ new Grassmann time variables $胃_k$ are introduced, and the Hamiltonian is represented as a differential operator acting on a space of functions of both types of variables $p_k$ and $胃_k$. Eigenfunctions for this Hamiltonian are a suitable generalization of Macdonald polynomials to super-Macdonald polynomials discussed earlier in the literature. Peculiarities of the construction in comparison to the canonical bosonic case are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.14714v1-abstract-full').style.display = 'none'; document.getElementById('2501.14714v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.20931">arXiv:2412.20931</a> <span> [<a href="https://arxiv.org/pdf/2412.20931">pdf</a>, <a href="https://arxiv.org/format/2412.20931">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Entangling gates from cabling of knots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+S">Sergey Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.20931v2-abstract-short" style="display: inline;"> While there is a general consensus about the structure of one qubit operations in topological quantum computer, two qubits are as usual a more difficult and complex story of different attempts with varying approaches, problems and effectiveness. In this paper we discuss how to construct an efficient realization of a two qubit gate in topological quantum computer, by using principle of cabling from… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20931v2-abstract-full').style.display = 'inline'; document.getElementById('2412.20931v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.20931v2-abstract-full" style="display: none;"> While there is a general consensus about the structure of one qubit operations in topological quantum computer, two qubits are as usual a more difficult and complex story of different attempts with varying approaches, problems and effectiveness. In this paper we discuss how to construct an efficient realization of a two qubit gate in topological quantum computer, by using principle of cabling from the knot theory. This allows to construct a braiding of cables dependent on the parameters of the theory where there is a low probability of moving out of computational space (high fidelity of operation) while there is a non-trivial entangling two-qubit operation. We also present some examples of these operations for different parameters of the theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20931v2-abstract-full').style.display = 'none'; document.getElementById('2412.20931v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-41/24, IITP/TH-35/24, MIPT/TH-25/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.19588">arXiv:2412.19588</a> <span> [<a href="https://arxiv.org/pdf/2412.19588">pdf</a>, <a href="https://arxiv.org/ps/2412.19588">ps</a>, <a href="https://arxiv.org/format/2412.19588">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Elliptic triad </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Zakirova%2C+Z">Z. Zakirova</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.19588v1-abstract-short" style="display: inline;"> The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of $t$. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we dis… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.19588v1-abstract-full').style.display = 'inline'; document.getElementById('2412.19588v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.19588v1-abstract-full" style="display: none;"> The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of $t$. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we discuss various possible approaches, including immediate elliptic deformation of periodicity conditions, (elliptic) Ding-Iohara-Miki algebra operators, and elliptic Kostka coefficients. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.19588v1-abstract-full').style.display = 'none'; document.getElementById('2412.19588v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-24/24; FIAN/TD-15/24; ITEP/TH-39/24; IITP/TH-33/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.16517">arXiv:2411.16517</a> <span> [<a href="https://arxiv.org/pdf/2411.16517">pdf</a>, <a href="https://arxiv.org/ps/2411.16517">ps</a>, <a href="https://arxiv.org/format/2411.16517">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> A basic triad in Macdonald theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.16517v1-abstract-short" style="display: inline;"> Within the context of wavefunctions of integrable many-body systems, rational multivariable Baker-Akhiezer (BA) functions were introduced by O. Chalykh, M. Feigin and A. Veselov and, in the case of the trigonometric Ruijsenaars-Schneider system, can be associated with a reduction of the Macdonald symmetric polynomials at $t=q^{-m}$ with integer partition labels substituted by arbitrary complex num… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.16517v1-abstract-full').style.display = 'inline'; document.getElementById('2411.16517v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.16517v1-abstract-full" style="display: none;"> Within the context of wavefunctions of integrable many-body systems, rational multivariable Baker-Akhiezer (BA) functions were introduced by O. Chalykh, M. Feigin and A. Veselov and, in the case of the trigonometric Ruijsenaars-Schneider system, can be associated with a reduction of the Macdonald symmetric polynomials at $t=q^{-m}$ with integer partition labels substituted by arbitrary complex numbers. A parallel attempt to describe wavefunctions of the bispectral trigonometric Ruijsenaars-Schneider problem was made by M. Noumi and J. Shiraishi who proposed a power series that reduces to the Macdonald polynomials at particular values of parameters. It turns out that this power series also reduces to the BA functions at $t=q^{-m}$, as we demonstrate in this letter. This makes the Macdonald polynomials, the BA functions and the Noumi-Shiraishi (NS) series a closely tied {\it triad} of objects, which have very different definitions, but are straightforwardly related with each other. In particular, theory of the BA functions provides a nice system of simple linear equations, while the NS functions provide a nice way to represent the multivariable BA function explicitly with arbitrary number of variables. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.16517v1-abstract-full').style.display = 'none'; document.getElementById('2411.16517v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-28/24; FIAN/TD-16/24; ITEP/TH-36/24; IITP/TH-31/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.14194">arXiv:2411.14194</a> <span> [<a href="https://arxiv.org/pdf/2411.14194">pdf</a>, <a href="https://arxiv.org/ps/2411.14194">ps</a>, <a href="https://arxiv.org/format/2411.14194">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2025.116809">10.1016/j.nuclphysb.2025.116809 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Chalykh's Baker-Akhiezer functions as eigenfunctions of the integer-ray integrable systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.14194v1-abstract-short" style="display: inline;"> Macdonald symmetric polynomial at $t=q^{-m}$ reduces to a sum of much simpler complementary non-symmetric polynomials, which satisfy a simple system of the first order linear difference equations with constant coefficients, much simpler than those induced by the usual Ruijsenaars Hamiltonians of the cut-and-join type. We provide examples of explicit expressions for these polynomials nicknamed Bake… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.14194v1-abstract-full').style.display = 'inline'; document.getElementById('2411.14194v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.14194v1-abstract-full" style="display: none;"> Macdonald symmetric polynomial at $t=q^{-m}$ reduces to a sum of much simpler complementary non-symmetric polynomials, which satisfy a simple system of the first order linear difference equations with constant coefficients, much simpler than those induced by the usual Ruijsenaars Hamiltonians of the cut-and-join type. We provide examples of explicit expressions for these polynomials nicknamed Baker-Akhiezer functions (BAF), and demonstrate that they further decompose into sums of nicely factorized quantities, perhaps, non-uniquely. Equations and solutions can be easily continued to non-integer parameters $位$, which, in Macdonald polynomial case, are associated with integer partitions. Moreover, there is a straightforward generalization to "twisted" BAF's, which, however, are not so easy to decompose, and factorization of the coefficients is lost, at least naively. Still, these twisted BAF's provide eigenfunctions for Hamiltonians associated with commutative integer ray subalgebras of the Ding-Iohara-Miki algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.14194v1-abstract-full').style.display = 'none'; document.getElementById('2411.14194v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-24/24; FIAN/TD-15/24; ITEP/TH-30/24; IITP/TH-25/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B1012 (2025) 116809 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.18525">arXiv:2410.18525</a> <span> [<a href="https://arxiv.org/pdf/2410.18525">pdf</a>, <a href="https://arxiv.org/format/2410.18525">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Planar decomposition of bipartite HOMFLY polynomials in symmetric representations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Anokhina%2C+A">A. Anokhina</a>, <a href="/search/hep-th?searchtype=author&query=Lanina%2C+E">E. Lanina</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.18525v1-abstract-short" style="display: inline;"> We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polynomials. Cabling destroys planarity, but it is restored after projection to (anti)symmetric representations. This allows to go beyond arborescent calculus, which so far produced the majority of results for colored polynom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.18525v1-abstract-full').style.display = 'inline'; document.getElementById('2410.18525v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.18525v1-abstract-full" style="display: none;"> We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polynomials. Cabling destroys planarity, but it is restored after projection to (anti)symmetric representations. This allows to go beyond arborescent calculus, which so far produced the majority of results for colored polynomials. Technicalities include combinations of projectors, and these can be handled rigorously, without any guess-work -- what can be also useful for other considerations, where reliable quantization was so far unavailable. We explicitly provide simple examples of calculation of the HOMFLY polynomials in symmetric representations with the use of our planar technique. These examples reveal what we call the bipartite evolution and the bipartite decomposition of squares of $\mathcal{R}$-matrices eigenvalues in the antiparallel channel. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.18525v1-abstract-full').style.display = 'none'; document.getElementById('2410.18525v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.13676">arXiv:2410.13676</a> <span> [<a href="https://arxiv.org/pdf/2410.13676">pdf</a>, <a href="https://arxiv.org/ps/2410.13676">ps</a>, <a href="https://arxiv.org/format/2410.13676">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">Aleksandr Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Sleptsov%2C+A">Alexei Sleptsov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.13676v2-abstract-short" style="display: inline;"> We prove that normalized colored Alexander polynomial (the $A \rightarrow 1$ limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution $q \rightarrow q^{|R|}$. The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.13676v2-abstract-full" style="display: none;"> We prove that normalized colored Alexander polynomial (the $A \rightarrow 1$ limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution $q \rightarrow q^{|R|}$. The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.13676v2-abstract-full').style.display = 'none'; document.getElementById('2410.13676v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.10685">arXiv:2410.10685</a> <span> [<a href="https://arxiv.org/pdf/2410.10685">pdf</a>, <a href="https://arxiv.org/ps/2410.10685">ps</a>, <a href="https://arxiv.org/format/2410.10685">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.10685v1-abstract-short" style="display: inline;"> Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer funct… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.10685v1-abstract-full').style.display = 'inline'; document.getElementById('2410.10685v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.10685v1-abstract-full" style="display: none;"> Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.10685v1-abstract-full').style.display = 'none'; document.getElementById('2410.10685v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, LaTeX</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-23/24; FIAN/TD-14/24; ITEP/TH-29/24; IITP/TH-24/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.03175">arXiv:2410.03175</a> <span> [<a href="https://arxiv.org/pdf/2410.03175">pdf</a>, <a href="https://arxiv.org/ps/2410.03175">ps</a>, <a href="https://arxiv.org/format/2410.03175">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.110.126026">10.1103/PhysRevD.110.126026 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> CMM formula as superintegrability property of unitary model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.03175v2-abstract-short" style="display: inline;"> A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT polynomial and a pair of the Schur functions, it is a relation in the unitary matrix model. We explain that the Cherednik-Mehta-Macdonald (CMM) identity for bil… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.03175v2-abstract-full').style.display = 'inline'; document.getElementById('2410.03175v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.03175v2-abstract-full" style="display: none;"> A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT polynomial and a pair of the Schur functions, it is a relation in the unitary matrix model. We explain that the Cherednik-Mehta-Macdonald (CMM) identity for bilinear Macdonald residues with an elliptic weight function is nothing but a reformulation of these same formulas. Their lifting to arbitrary knots and links, even torus ones remains obscure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.03175v2-abstract-full').style.display = 'none'; document.getElementById('2410.03175v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-22/24; FIAN/TD-11/24; ITEP/TH-28/24; IITP/TH-23/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 110 (2024) 126026 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.15724">arXiv:2408.15724</a> <span> [<a href="https://arxiv.org/pdf/2408.15724">pdf</a>, <a href="https://arxiv.org/ps/2408.15724">ps</a>, <a href="https://arxiv.org/format/2408.15724">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Banana diagrams as functions of geodesic distance </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Diakonov%2C+D">D. Diakonov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.15724v1-abstract-short" style="display: inline;"> We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be express… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.15724v1-abstract-full').style.display = 'inline'; document.getElementById('2408.15724v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.15724v1-abstract-full" style="display: none;"> We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be expressed as determinants of certain operators. Therefore, not-surprisingly, the coordinate equations remain straightforward -- while their reformulation in terms of momentum integrals and Picard-Fuchs equations can seem problematic. However we show that the Feynman parameter representation can also be generalized, at least for banana diagrams in simple harmonic spaces, so that the Picard-Fuchs equations retain their Euclidean form with just a minor modification. A separate story is the transfer to the case when the Green function essentially depends on several rather than a single argument. In this case, we provide just one example, that the equations are still there, but conceptual issues in the more general case will be discussed elsewhere. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.15724v1-abstract-full').style.display = 'none'; document.getElementById('2408.15724v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.14188">arXiv:2408.14188</a> <span> [<a href="https://arxiv.org/pdf/2408.14188">pdf</a>, <a href="https://arxiv.org/format/2408.14188">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Measuring Chern-Simons level $k$ by braiding $SU(2)_k$ anyons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Belov%2C+A">Artem Belov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.14188v1-abstract-short" style="display: inline;"> Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern-Simons level $k$ in the unknown material. For this purpose, we use the previously derived braiding rul… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.14188v1-abstract-full').style.display = 'inline'; document.getElementById('2408.14188v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.14188v1-abstract-full" style="display: none;"> Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern-Simons level $k$ in the unknown material. For this purpose, we use the previously derived braiding rules for Chern-Simons $SU(2)_k$ anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern-Simons level $k$ can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.14188v1-abstract-full').style.display = 'none'; document.getElementById('2408.14188v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 13 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-31/24 IITP/TH-26/24 MIPT/TH-25/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.08181">arXiv:2408.08181</a> <span> [<a href="https://arxiv.org/pdf/2408.08181">pdf</a>, <a href="https://arxiv.org/format/2408.08181">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2024.139139">10.1016/j.physletb.2024.139139 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On geometric bases for quantum A-polynomials of knots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.08181v2-abstract-short" style="display: inline;"> A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid over… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.08181v2-abstract-full').style.display = 'inline'; document.getElementById('2408.08181v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.08181v2-abstract-full" style="display: none;"> A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.08181v2-abstract-full').style.display = 'none'; document.getElementById('2408.08181v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, v2: minor updates</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B 860 (2025) 139139 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.21200">arXiv:2407.21200</a> <span> [<a href="https://arxiv.org/pdf/2407.21200">pdf</a>, <a href="https://arxiv.org/format/2407.21200">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Position space equations for generic Feynman graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Reva%2C+M">M. Reva</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.21200v1-abstract-short" style="display: inline;"> We propose the extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on getting rid of integration in position space and then writing differential equations for the products of propagators defined for any graph. We employ the so-called ''bananization'' to start with simple Feynman graphs and further substituting each… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.21200v1-abstract-full').style.display = 'inline'; document.getElementById('2407.21200v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.21200v1-abstract-full" style="display: none;"> We propose the extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on getting rid of integration in position space and then writing differential equations for the products of propagators defined for any graph. We employ the so-called ''bananization'' to start with simple Feynman graphs and further substituting each edge with a multiple one. We explain how the previously developed theory of banana diagrams can be used to describe what happens to the differential equations (Ward identities) on Feynman diagrams after this transformation. Our approach works for generic enough (large enough) dimension and masses. We expect that after Fourier transform our equations should be related to the Picard-Fuchs equations. Therefore, we describe the challenges of Fourier transform that arise in our approach. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.21200v1-abstract-full').style.display = 'none'; document.getElementById('2407.21200v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MITP-TH-18/24, ITEP-TH-24/24, IITP-TH-19/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.08724">arXiv:2407.08724</a> <span> [<a href="https://arxiv.org/pdf/2407.08724">pdf</a>, <a href="https://arxiv.org/format/2407.08724">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epjc/s10052-024-13309-0">10.1140/epjc/s10052-024-13309-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Planar decomposition of the HOMFLY polynomial for bipartite knots and links </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Anokhina%2C+A">A. Anokhina</a>, <a href="/search/hep-th?searchtype=author&query=Lanina%2C+E">E. Lanina</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.08724v2-abstract-short" style="display: inline;"> The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straightforwardly lifted from sl(2) to sl(N) at arbitrary N -- but for a special class of bipartite diagrams made entirely from the anitparallel lock tangle. Many amusing and important knots and links can be described in this wa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.08724v2-abstract-full').style.display = 'inline'; document.getElementById('2407.08724v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.08724v2-abstract-full" style="display: none;"> The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straightforwardly lifted from sl(2) to sl(N) at arbitrary N -- but for a special class of bipartite diagrams made entirely from the anitparallel lock tangle. Many amusing and important knots and links can be described in this way, from twist and double braid knots to the celebrated Kanenobu knots for even parameters -- and for all of them the entire HOMFLY polynomials possess planar decomposition. This provides an approach to evaluation of HOMFLY polynomials, which is complementary to the arborescent calculus, and this opens a new direction to homological techniques, parallel to Khovanov-Rozansky generalisations of the Kauffman calculus. Moreover, this planar calculus is also applicable to other symmetric representations beyond the fundamental one, and to links which are not fully bipartite what is illustrated by examples of Kanenobu-like links. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.08724v2-abstract-full').style.display = 'none'; document.getElementById('2407.08724v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">33 pages, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> The European Physical Journal C 84 (2024) 990 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.04810">arXiv:2407.04810</a> <span> [<a href="https://arxiv.org/pdf/2407.04810">pdf</a>, <a href="https://arxiv.org/ps/2407.04810">ps</a>, <a href="https://arxiv.org/format/2407.04810">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.21468/SciPostPhys.17.4.119">10.21468/SciPostPhys.17.4.119 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Supersymmetric polynomials and algebro-combinatorial duality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.04810v2-abstract-short" style="display: inline;"> In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend on odd Grassmann variables as well. Members of these families are labeled by respective modifications of Young diagrams. We show that the super-Macdonald polynom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.04810v2-abstract-full').style.display = 'inline'; document.getElementById('2407.04810v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.04810v2-abstract-full" style="display: none;"> In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend on odd Grassmann variables as well. Members of these families are labeled by respective modifications of Young diagrams. We show that the super-Macdonald polynomials form a representation of a super-algebra analog $\mathsf{T}(\widehat{\mathfrak{gl}}_{1|1})$ of Ding-Ioahara-Miki (quantum toroidal) algebra, emerging as a BPS algebra of D-branes on a conifold. A supersymmetric modification for Young tableaux and Kostka numbers are also discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.04810v2-abstract-full').style.display = 'none'; document.getElementById('2407.04810v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages, 2 figures, v2: typos corrected, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SciPost Phys. 17, 119 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.03301">arXiv:2407.03301</a> <span> [<a href="https://arxiv.org/pdf/2407.03301">pdf</a>, <a href="https://arxiv.org/ps/2407.03301">ps</a>, <a href="https://arxiv.org/format/2407.03301">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2024.138911">10.1016/j.physletb.2024.138911 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Macdonald polynomials for super-partitions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.03301v1-abstract-short" style="display: inline;"> We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $胃_k$. Starting from recently defined super-Schur polynomials and exploiting orthogon… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.03301v1-abstract-full').style.display = 'inline'; document.getElementById('2407.03301v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.03301v1-abstract-full" style="display: none;"> We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $胃_k$. Starting from recently defined super-Schur polynomials and exploiting orthogonality relations with triangular decompositions we are able to fully determine super-Macdonald polynomials. These new polynomials have similar properties to canonical Macdonald polynomials -- they respect two different orderings in the set of (super)-Young diagrams simultaneously. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.03301v1-abstract-full').style.display = 'none'; document.getElementById('2407.03301v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.20074">arXiv:2406.20074</a> <span> [<a href="https://arxiv.org/pdf/2406.20074">pdf</a>, <a href="https://arxiv.org/ps/2406.20074">ps</a>, <a href="https://arxiv.org/format/2406.20074">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP08(2024)209">10.1007/JHEP08(2024)209 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Algorithms for representations of quiver Yangian algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Gavshin%2C+A">Alexei Gavshin</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.20074v1-abstract-short" style="display: inline;"> In this note, we aim to review algorithms for constructing crystal representations of quiver Yangians in detail. Quiver Yangians are believed to describe an action of the BPS algebra on BPS states in systems of D-branes wrapping toric Calabi-Yau three-folds. Crystal modules of these algebras originate from molten crystal models for Donaldson-Thomas invariants of respective three-folds. Despite the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.20074v1-abstract-full').style.display = 'inline'; document.getElementById('2406.20074v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.20074v1-abstract-full" style="display: none;"> In this note, we aim to review algorithms for constructing crystal representations of quiver Yangians in detail. Quiver Yangians are believed to describe an action of the BPS algebra on BPS states in systems of D-branes wrapping toric Calabi-Yau three-folds. Crystal modules of these algebras originate from molten crystal models for Donaldson-Thomas invariants of respective three-folds. Despite the fact that this subject was originally at the crossroads of algebraic geometry with effective supersymmetric field theories, equivariant toric action simplifies applied calculations drastically. So the sole pre-requisite for this algorithm's implementation is linear algebra. It can be easily taught to a machine with the help of any symbolic calculation system. Moreover, these algorithms may be generalized to toroidal and elliptic algebras and exploited in various numerical experiments with those algebras. We illustrate the work of the algorithms in applications to simple cases of $\mathsf{Y}(\mathfrak{sl}_2)$, $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1})$ and $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.20074v1-abstract-full').style.display = 'none'; document.getElementById('2406.20074v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">41 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 08 (2024) 209 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.16688">arXiv:2406.16688</a> <span> [<a href="https://arxiv.org/pdf/2406.16688">pdf</a>, <a href="https://arxiv.org/ps/2406.16688">ps</a>, <a href="https://arxiv.org/format/2406.16688">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP09(2024)200">10.1007/JHEP09(2024)200 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.16688v2-abstract-short" style="display: inline;"> We extend our consideration of commutative subalgebras (rays) in different representations of the $W_{1+\infty}$ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$). Its advantage is that it possesses the Miki automorphism, which makes all commutative rays equivalent. Integrable systems associated with these… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.16688v2-abstract-full').style.display = 'inline'; document.getElementById('2406.16688v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.16688v2-abstract-full" style="display: none;"> We extend our consideration of commutative subalgebras (rays) in different representations of the $W_{1+\infty}$ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$). Its advantage is that it possesses the Miki automorphism, which makes all commutative rays equivalent. Integrable systems associated with these rays become finite-difference and, apart from the trigonometric Ruijsenaars system not too much familiar. We concentrate on the simplest many-body and Fock representations, and derive explicit formulas for all generators of the elliptic Hall algebra $e_{n,m}$. In the one-body representation, they differ just by normalization from $z^nq^{m\hat D}$ of the $W_{1+\infty}$ Lie algebra, and, in the $N$-body case, they are non-trivially generalized to monomials of the Cherednik operators with action restricted to symmetric polynomials. In the Fock representation, the resulting operators are expressed through auxiliary polynomials of $n$ variables, which define weights in the residues formulas. We also discuss $q,t$-deformation of matrix models associated with constructed commutative subalgebras. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.16688v2-abstract-full').style.display = 'none'; document.getElementById('2406.16688v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">51 pages, LaTeX</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-07/24; IITP/TH-13/24; ITEP/TH-15/24; MIPT/TH-11/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2024 (2024) 200 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.13579">arXiv:2405.13579</a> <span> [<a href="https://arxiv.org/pdf/2405.13579">pdf</a>, <a href="https://arxiv.org/ps/2405.13579">ps</a>, <a href="https://arxiv.org/format/2405.13579">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2024.139006">10.1016/j.physletb.2024.139006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On character expansion and Gaussian regularization of Itzykson-Zuber measure </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Oreshina%2C+A">A. Oreshina</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.13579v1-abstract-short" style="display: inline;"> Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various deformations, which are not transparent in integral formulation. We analyze from this point of view the Itzykson-Zuber integral over unitary matrices which is exactly solva… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13579v1-abstract-full').style.display = 'inline'; document.getElementById('2405.13579v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.13579v1-abstract-full" style="display: none;"> Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various deformations, which are not transparent in integral formulation. We analyze from this point of view the Itzykson-Zuber integral over unitary matrices which is exactly solvable, but difficult to deform in $尾$ and $(q,t)$ directions. Character expansion straightforwardly resolves this problem. However, taking averages with the so defined measure can look problematic, because integrals of individual expansion terms often diverge and well defined is only the sum of them. We explain a way to overcome this problem by Gaussian regularization, which can have a broad range of further applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13579v1-abstract-full').style.display = 'none'; document.getElementById('2405.13579v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-05/24; IITP/TH-05/24; ITEP/TH-06/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Letters B, Volume 857, 2024, 139006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.03645">arXiv:2405.03645</a> <span> [<a href="https://arxiv.org/pdf/2405.03645">pdf</a>, <a href="https://arxiv.org/format/2405.03645">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Calculating HOMFLY-PT polynomials on a photonic processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Dyakonov%2C+I">Ivan Dyakonov</a>, <a href="/search/hep-th?searchtype=author&query=Kondratyev%2C+I">Ilya Kondratyev</a>, <a href="/search/hep-th?searchtype=author&query=Mironov%2C+S">Sergey Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.03645v1-abstract-short" style="display: inline;"> In this paper we discuss an approach to calculate knot polynomials on a photonic processor. Calculations of knot polynomials is a computationally difficult problem and therefore it is interesting to use new advanced calculation methods to find them. Here we present a proof of concept by calculating the simplest knot polynomial of the trefoil knot in fundamental representation. This approach, howev… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.03645v1-abstract-full').style.display = 'inline'; document.getElementById('2405.03645v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.03645v1-abstract-full" style="display: none;"> In this paper we discuss an approach to calculate knot polynomials on a photonic processor. Calculations of knot polynomials is a computationally difficult problem and therefore it is interesting to use new advanced calculation methods to find them. Here we present a proof of concept by calculating the simplest knot polynomial of the trefoil knot in fundamental representation. This approach, however, can easily be generalized to more complex knots and representations. Same operators can also be realized on a quantum computer with the same effect. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.03645v1-abstract-full').style.display = 'none'; document.getElementById('2405.03645v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-13/24 IITP/TH-11/24 MIPT/TH-9/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.12222">arXiv:2404.12222</a> <span> [<a href="https://arxiv.org/pdf/2404.12222">pdf</a>, <a href="https://arxiv.org/format/2404.12222">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.110.126020">10.1103/PhysRevD.110.126020 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Entangled states from arborescent knots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+S">Sergey Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2404.12222v2-abstract-short" style="display: inline;"> In this paper we discuss how to use arborescent knots to construct entangled multi-qubit states. We show that Bell-states, GHZ-states and cluster states can be constructed from such knots. The latter are particularly interesting since they form a base for the measurement-based quantum computers. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.12222v2-abstract-full" style="display: none;"> In this paper we discuss how to use arborescent knots to construct entangled multi-qubit states. We show that Bell-states, GHZ-states and cluster states can be constructed from such knots. The latter are particularly interesting since they form a base for the measurement-based quantum computers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.12222v2-abstract-full').style.display = 'none'; document.getElementById('2404.12222v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-12/24 IITP/TH-10/24 MIPT/TH-8/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 110, 126020, 2024 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.03069">arXiv:2404.03069</a> <span> [<a href="https://arxiv.org/pdf/2404.03069">pdf</a>, <a href="https://arxiv.org/format/2404.03069">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> From equations in coordinate space to Picard-Fuchs and back </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Reva%2C+M">M. Reva</a>, <a href="/search/hep-th?searchtype=author&query=Suprun%2C+P">P. Suprun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2404.03069v1-abstract-short" style="display: inline;"> We continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum space. The natural place to start are the famous banana diagrams, which we explore in this paper. In position space, these are just products of $n$ propagators. Fi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.03069v1-abstract-full').style.display = 'inline'; document.getElementById('2404.03069v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.03069v1-abstract-full" style="display: none;"> We continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum space. The natural place to start are the famous banana diagrams, which we explore in this paper. In position space, these are just products of $n$ propagators. Firstly, we explain that these functions satisfy an equation of order $2^n$. These should be compared with Picard-Fuchs equations derived for the momentum space integral. We find that the Fourier transform of the position space operator contains the Picard-Fuchs one as a rightmost factor. The order of these operators is a special issue, especially since the order in momentum space is governed by degree in $x$ in position space. For the generic mass case this factorization pattern is complicated and it seems like the order of the Fourier transformed position space operators is much bigger than that of the Picard-Fuchs. Furthermore, one may ask what happens if after factorization we take the Picard-Fuchs operators back into position space. We discover that the result is again factorized, with the rightmost factor being the original position space equation. We demonstrate how this works in examples and discuss implications for more sophisticated Feynman integrals. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.03069v1-abstract-full').style.display = 'none'; document.getElementById('2404.03069v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.14600">arXiv:2403.14600</a> <span> [<a href="https://arxiv.org/pdf/2403.14600">pdf</a>, <a href="https://arxiv.org/ps/2403.14600">ps</a>, <a href="https://arxiv.org/format/2403.14600">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP05(2024)118">10.1007/JHEP05(2024)118 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Wall-Crossing Effects on Quiver BPS Algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.14600v2-abstract-short" style="display: inline;"> BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module, and matrix elements for the generators are then defined as Duistermaat-Heckman integrals in the vicinity of these points. The well-known wall-cros… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.14600v2-abstract-full').style.display = 'inline'; document.getElementById('2403.14600v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.14600v2-abstract-full" style="display: none;"> BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module, and matrix elements for the generators are then defined as Duistermaat-Heckman integrals in the vicinity of these points. The well-known wall-crossing phenomena are that the fixed point spectrum establishes a dependence on the stability (Fayet-Illiopolous) parameters $味$, jumping abruptly across the walls of marginal stability, which divide the $味$-space into a collection of stability chambers -- ``phases'' of the theory. The standard construction of the quiver Yangian algebra relies heavily on the molten crystal model, valid in a sole cyclic chamber where all the $味$-parameters have the same sign. We propose to lift this restriction and investigate the effects of the wall-crossing phenomena on the quiver Yangian algebra and its representations -- starting with the example of affine super-Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. In addition to the molten crystal construction more general atomic structures appear, in other non-cyclic phases (chambers of the $味$-space). We call them glasses and also divide in a few different classes. For some of the new phases we manage to associate an algebraic structure again as a representation of the same affine Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. This observation supports an earlier conjecture that the BPS algebraic structures can be considered as new wall-crossing invariants. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.14600v2-abstract-full').style.display = 'none'; document.getElementById('2403.14600v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">36 pages, 7 figures, minor corrections, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP05(2024)118 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.09670">arXiv:2403.09670</a> <span> [<a href="https://arxiv.org/pdf/2403.09670">pdf</a>, <a href="https://arxiv.org/format/2403.09670">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.110.046027">10.1103/PhysRevD.110.046027 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Deformation of superintegrability in the Miwa-deformed Gaussian matrix model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Shakirov%2C+S">Sh. Shakirov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.09670v2-abstract-short" style="display: inline;"> We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a {\it finite degree} polynomial made from the values of sk… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09670v2-abstract-full').style.display = 'inline'; document.getElementById('2403.09670v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.09670v2-abstract-full" style="display: none;"> We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a {\it finite degree} polynomial made from the values of skew Schur functions at the Gaussian locus $p_k=未_{k,2}$. This linear operation includes multiplication with an exponential $ e^{z_a^2/2}$ and a kind of Borel transform of the resulting product, which we call multiple and enhanced. The existence of such remarkable formulas appears intimately related to the theory of auxiliary $K$-polynomials, which appeared in {\it bilinear} superintegrable correlators at the Gaussian point (strict superintegrability). We also consider in the very detail the generating function of correlators $<(\Tr X)^k>$ in this model, and discuss its integrable determinant representation. At last, we describe deformation of all results to the Gaussian $尾$-ensemble. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09670v2-abstract-full').style.display = 'none'; document.getElementById('2403.09670v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages. arXiv admin note: text overlap with arXiv:2401.14392</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-03/24; IITP/TH-04/24; ITEP/TH-05/24; MIPT/TH-04/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 110 (2024) 046027 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.07847">arXiv:2403.07847</a> <span> [<a href="https://arxiv.org/pdf/2403.07847">pdf</a>, <a href="https://arxiv.org/format/2403.07847">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1134/S0032946024010046">10.1134/S0032946024010046 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On measuring the topological charge of anyons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.07847v1-abstract-short" style="display: inline;"> In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show how it can be modified to be more effective for different levels of Chern-Simons theory. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.07847v1-abstract-full" style="display: none;"> In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show how it can be modified to be more effective for different levels of Chern-Simons theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.07847v1-abstract-full').style.display = 'none'; document.getElementById('2403.07847v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-9/24 IITP/TH-8/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Problems of Information Transmission 60, 28-34 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.05920">arXiv:2402.05920</a> <span> [<a href="https://arxiv.org/pdf/2402.05920">pdf</a>, <a href="https://arxiv.org/ps/2402.05920">ps</a>, <a href="https://arxiv.org/format/2402.05920">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epjc/s10052-024-12952-x">10.1140/epjc/s10052-024-12952-x <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Simple Representations of BPS Algebras: the case of $Y(\widehat{\mathfrak{gl}}_2)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.05920v2-abstract-short" style="display: inline;"> BPS algebras are the symmetries of a wide class of brane-inspired models. They are closely related to Yangians -- the peculiar and somewhat sophisticated limit of DIM algebras. Still they possess some simple and explicit representations. We explain here that for $Y(\widehat{\mathfrak{gl}}_r)$ these representations are related to Uglov polynomials, whose families are also labeled by natural $r$. Th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.05920v2-abstract-full').style.display = 'inline'; document.getElementById('2402.05920v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.05920v2-abstract-full" style="display: none;"> BPS algebras are the symmetries of a wide class of brane-inspired models. They are closely related to Yangians -- the peculiar and somewhat sophisticated limit of DIM algebras. Still they possess some simple and explicit representations. We explain here that for $Y(\widehat{\mathfrak{gl}}_r)$ these representations are related to Uglov polynomials, whose families are also labeled by natural $r$. They arise in the limit $\hbar\longrightarrow 0$ from Macdonald polynomials, and generalize the well-known Jack polynomials ($尾$-deformation of Schur functions), associated with $r=1$. For $r=2$ they approximate Macdonald polynomials with the accuracy $O(\hbar^2)$, so that they are eigenfunctions of {\it two} immediately available commuting operators, arising from the $\hbar$-expansion of the first Macdonald Hamiltonian. These operators have a clear structure, which is easily generalizable, -- what provides a technically simple way to build an explicit representation of Yangian $Y(\widehat{\mathfrak{gl}}_2)$, where $U^{(2)}$ are associated with the states $|位\rangle$, parametrized by chess-colored Young diagrams. An interesting feature of this representation is that the odd time-variables $p_{2n+1}$ can be expressed through mutually commuting operators from Yangian, however even time-variables $p_{2n}$ are inexpressible. Implications to higher $r$ become now straightforward, yet we describe them only in a sketchy way. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.05920v2-abstract-full').style.display = 'none'; document.getElementById('2402.05920v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.14392">arXiv:2401.14392</a> <span> [<a href="https://arxiv.org/pdf/2401.14392">pdf</a>, <a href="https://arxiv.org/format/2401.14392">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2024.138593">10.1016/j.physletb.2024.138593 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Summing up perturbation series around superintegrable point </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Shakirov%2C+S">Sh. Shakirov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.14392v1-abstract-short" style="display: inline;"> We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions $S_Q$ is an explicit function of the Young diagram $Q$. The question is what happens to this… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.14392v1-abstract-full').style.display = 'inline'; document.getElementById('2401.14392v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.14392v1-abstract-full" style="display: none;"> We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions $S_Q$ is an explicit function of the Young diagram $Q$. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on $R$ enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call ``truncation'' of the Young diagram $Q$. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.14392v1-abstract-full').style.display = 'none'; document.getElementById('2401.14392v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages + Appendix (7 pages)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-02/24; IITP/TH-01/24; ITEP/TH-01/24; MIPT/TH-01/24 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett. B852 (2024) 138593 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.00695">arXiv:2312.00695</a> <span> [<a href="https://arxiv.org/pdf/2312.00695">pdf</a>, <a href="https://arxiv.org/format/2312.00695">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2024.116504">10.1016/j.nuclphysb.2024.116504 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tau-functions beyond the group elements </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.00695v1-abstract-short" style="display: inline;"> Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $螖(X) = X\otimes X$, then their generating functions obey bilinear Hirota equations and hence are named $蟿$-functions. However, dealing with group elements is not always easy, especially for non-commutative algebras of functions… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.00695v1-abstract-full').style.display = 'inline'; document.getElementById('2312.00695v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.00695v1-abstract-full" style="display: none;"> Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $螖(X) = X\otimes X$, then their generating functions obey bilinear Hirota equations and hence are named $蟿$-functions. However, dealing with group elements is not always easy, especially for non-commutative algebras of functions, and this slows down the development of $蟿$-function theory and the study of integrability properties of non-perturbative functional integrals. A simple way out is to use arbitrary elements of the universal enveloping algebra, and not just the group elements. Then the Hirota equations appear to interrelate a whole system of generating functions, which one may call $\textit{generalized}$ $蟿$-functions. It was recently demonstrated that this idea can be applicable even to a somewhat sophisticated case of the quantum toroidal algebra. We consider a number of simpler examples, including ordinary and quantum groups, to explain how the method works and what kind of solutions one can obtain. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.00695v1-abstract-full').style.display = 'none'; document.getElementById('2312.00695v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-15/23, IITP/TH-21/23, ITEP/TH-27/23, MIPT/TH-20/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B1001 (2024) 116504 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.13524">arXiv:2311.13524</a> <span> [<a href="https://arxiv.org/pdf/2311.13524">pdf</a>, <a href="https://arxiv.org/format/2311.13524">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> On factorization hierarchy of equations for banana Feynman amplitudes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Reva%2C+M">M. Reva</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2311.13524v1-abstract-short" style="display: inline;"> We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with $未$-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First, we revie… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.13524v1-abstract-full').style.display = 'inline'; document.getElementById('2311.13524v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.13524v1-abstract-full" style="display: none;"> We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with $未$-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First, we review the properties of the corresponding differential operators themselves, mainly their factorization properties at the equal mass locus and their form at special values of the dimension. Then we study the relation between the Fourier transform of the coordinate space equations and the Picard-Fuchs equations and show that they are related by factorization as well. The equations in question are the counterparts of the Virasoro constraints in the much-better studied theory of eigenvalue matrix models and are the first step towards building a full-fledged theory of Feynman integrals, which will reveal their hidden integrable structure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.13524v1-abstract-full').style.display = 'none'; document.getElementById('2311.13524v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-17/23 IITP/TH-16/23 ITEP/TH-22/23 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.00760">arXiv:2311.00760</a> <span> [<a href="https://arxiv.org/pdf/2311.00760">pdf</a>, <a href="https://arxiv.org/ps/2311.00760">ps</a>, <a href="https://arxiv.org/format/2311.00760">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.109.066001">10.1103/PhysRevD.109.066001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards the theory of Yangians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2311.00760v1-abstract-short" style="display: inline;"> We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going generalization of simple Lie algebras classification by Dynkin diagrams. However, this is still a kind of project, while a more constructive approach goes through toric Calabi-Yau spaces, related supersymmetric systems and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00760v1-abstract-full').style.display = 'inline'; document.getElementById('2311.00760v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.00760v1-abstract-full" style="display: none;"> We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going generalization of simple Lie algebras classification by Dynkin diagrams. However, this is still a kind of project, while a more constructive approach goes through toric Calabi-Yau spaces, related supersymmetric systems and the Duistermaat-Heckmann/equivariant integrals between the fixed points in the ADHM-like moduli spaces. These fixed points are classified by crystals (Young-type diagrams) and Yangian generators describe ``instanton'' transitions between them. Detailed examples will be presented elsewhere. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00760v1-abstract-full').style.display = 'none'; document.getElementById('2311.00760v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 109, 066001 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.06403">arXiv:2309.06403</a> <span> [<a href="https://arxiv.org/pdf/2309.06403">pdf</a>, <a href="https://arxiv.org/ps/2309.06403">ps</a>, <a href="https://arxiv.org/format/2309.06403">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2024.116448">10.1016/j.nuclphysb.2024.116448 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the status of DELL systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.06403v2-abstract-short" style="display: inline;"> A detailed review of the $p,q$-duality for Calogero system and its generalizations is given. For the first time, we present some of elliptic-trigonometric Hamiltonians dual to the elliptic Ruijsenaars Hamiltonians (i.e. trigonometric-elliptic ones), and explain their relations to the bi-elliptic Koroteev-Shakirov (KS) model. The most interesting self-dual double-elliptic (DELL) system remains a my… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.06403v2-abstract-full').style.display = 'inline'; document.getElementById('2309.06403v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.06403v2-abstract-full" style="display: none;"> A detailed review of the $p,q$-duality for Calogero system and its generalizations is given. For the first time, we present some of elliptic-trigonometric Hamiltonians dual to the elliptic Ruijsenaars Hamiltonians (i.e. trigonometric-elliptic ones), and explain their relations to the bi-elliptic Koroteev-Shakirov (KS) model. The most interesting self-dual double-elliptic (DELL) system remains a mystery, but we provide a clearer formulation of the problem and describe the steps that are still to be done. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.06403v2-abstract-full').style.display = 'none'; document.getElementById('2309.06403v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX, 29 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-12/23; IITP/TH-14/23; ITEP/TH-20/23; MIPT/TH-15/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys. B999 (2024) 116448 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.13095">arXiv:2308.13095</a> <span> [<a href="https://arxiv.org/pdf/2308.13095">pdf</a>, <a href="https://arxiv.org/ps/2308.13095">ps</a>, <a href="https://arxiv.org/format/2308.13095">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2023.116403">10.1016/j.nuclphysb.2023.116403 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards tangle calculus for Khovanov polynomials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Anokhina%2C+A">A. Anokhina</a>, <a href="/search/hep-th?searchtype=author&query=Lanina%2C+E">E. Lanina</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2308.13095v1-abstract-short" style="display: inline;"> We provide new evidence that the tangle calculus and "evolution" are applicable to the Khovanov polynomials for families of long braids inside the knot diagram. We show that jumps in evolution, peculiar for superpolynomials, are much less abundant than it was originally expected. Namely, for torus and twist satellites of a fixed companion knot, the main (most complicated) contribution does not jum… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.13095v1-abstract-full').style.display = 'inline'; document.getElementById('2308.13095v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.13095v1-abstract-full" style="display: none;"> We provide new evidence that the tangle calculus and "evolution" are applicable to the Khovanov polynomials for families of long braids inside the knot diagram. We show that jumps in evolution, peculiar for superpolynomials, are much less abundant than it was originally expected. Namely, for torus and twist satellites of a fixed companion knot, the main (most complicated) contribution does not jump, all jumps are concentrated in the torus and twist part correspondingly, where these jumps are necessary to make the Khovanov polynomial positive. Among other things, this opens a way to define a jump-free part of the colored Khovanov polynomials, which differs from the naive colored polynomial just "infinitesimally". The separation between jumping and smooth parts involves a combination of Rasmussen index and a new knot invariant, which we call "Thickness". <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.13095v1-abstract-full').style.display = 'none'; document.getElementById('2308.13095v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 998 (2023) 116403 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.03150">arXiv:2307.03150</a> <span> [<a href="https://arxiv.org/pdf/2307.03150">pdf</a>, <a href="https://arxiv.org/ps/2307.03150">ps</a>, <a href="https://arxiv.org/format/2307.03150">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP08(2023)049">10.1007/JHEP08(2023)049 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galakhov%2C+D">Dmitry Galakhov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">Nikita Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.03150v2-abstract-short" style="display: inline;"> We explicitly construct cut-and-join operators and their eigenfunctions -- the Super-Schur functions -- for the case of the affine super-Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. This is the simplest non-trivial (semi-Fock) representation, where eigenfunctions are labeled by the superanalogue of 2d Young diagrams, and depend on the supertime variables $(p_k,胃_k)$. The action of other ge… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.03150v2-abstract-full').style.display = 'inline'; document.getElementById('2307.03150v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.03150v2-abstract-full" style="display: none;"> We explicitly construct cut-and-join operators and their eigenfunctions -- the Super-Schur functions -- for the case of the affine super-Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. This is the simplest non-trivial (semi-Fock) representation, where eigenfunctions are labeled by the superanalogue of 2d Young diagrams, and depend on the supertime variables $(p_k,胃_k)$. The action of other generators on diagrams is described by the analogue of the Pieri rule. As well we present generalizations of the hook formula for the measure on super-Young diagrams and of the Cauchy formula. Also a discussion of string theory origins for these relations is provided. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.03150v2-abstract-full').style.display = 'none'; document.getElementById('2307.03150v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP08(2023)049 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.01048">arXiv:2307.01048</a> <span> [<a href="https://arxiv.org/pdf/2307.01048">pdf</a>, <a href="https://arxiv.org/ps/2307.01048">ps</a>, <a href="https://arxiv.org/format/2307.01048">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2023.138122">10.1016/j.physletb.2023.138122 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Commutative subalgebras from Serre relations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.01048v1-abstract-short" style="display: inline;"> We demonstrate that commutativity of numerous one-dimensional subalgebras in $W_{1+\infty}$ algebra, i.e. the existence of many non-trivial integrable systems described in recent arXiv:2303.05273 follows from the subset of relations in algebra known as Serre relations. No other relations are needed for commutativity. The Serre relations survive the deformation to the affine Yangian… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.01048v1-abstract-full').style.display = 'inline'; document.getElementById('2307.01048v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.01048v1-abstract-full" style="display: none;"> We demonstrate that commutativity of numerous one-dimensional subalgebras in $W_{1+\infty}$ algebra, i.e. the existence of many non-trivial integrable systems described in recent arXiv:2303.05273 follows from the subset of relations in algebra known as Serre relations. No other relations are needed for commutativity. The Serre relations survive the deformation to the affine Yangian $Y(\hat{\mathfrak{gl}}_1)$, hence the commutative subalgebras do as well. A special case of the Yangian parameters corresponds to the $尾$-deformation. The preservation of Serre relations can be thought of a selection rule for proper systems of commuting $尾$-deformed Hamiltonians. On the contrary, commutativity in the extended family associated with ``rational (non-integer) rays" is {\it not} reduced to the Serre relations, and uses also other relations in the $W_{1+\infty}$ algebra. Thus their $尾$-deformation is less straightforward. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.01048v1-abstract-full').style.display = 'none'; document.getElementById('2307.01048v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-11/23; IITP/TH-12/23; ITEP/TH-16/23; MIPT/TH-13/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett. B845 (2023) 138122 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.06623">arXiv:2306.06623</a> <span> [<a href="https://arxiv.org/pdf/2306.06623">pdf</a>, <a href="https://arxiv.org/ps/2306.06623">ps</a>, <a href="https://arxiv.org/format/2306.06623">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP09(2023)065">10.1007/JHEP09(2023)065 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Commutative families in $W_\infty$, integrable many-body systems and hypergeometric $蟿$-functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.06623v3-abstract-short" style="display: inline;"> We explain that the set of new integrable systems generalizing the Calogero family and implied by the study of WLZZ models, which was described in arXiv:2303.05273, is only the tip of the iceberg. We provide its wide generalization and explain that it is related to commutative subalgebras (Hamiltonians) of the $W_{1+\infty}$ algebra. We construct many such subalgebras and explain how they look in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.06623v3-abstract-full').style.display = 'inline'; document.getElementById('2306.06623v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.06623v3-abstract-full" style="display: none;"> We explain that the set of new integrable systems generalizing the Calogero family and implied by the study of WLZZ models, which was described in arXiv:2303.05273, is only the tip of the iceberg. We provide its wide generalization and explain that it is related to commutative subalgebras (Hamiltonians) of the $W_{1+\infty}$ algebra. We construct many such subalgebras and explain how they look in various representations. We start from the even simpler $w_\infty$ contraction, then proceed to the one-body representation in terms of differential operators on a circle, further generalizing to matrices and in their eigenvalues, in finally to the bosonic representation in terms of time-variables. Moreover, we explain that some of the subalgebras survive the $尾$-deformation, an intermediate step from $W_{1+\infty}$ to the affine Yangian. The very explicit formulas for the corresponding Hamiltonians in these cases are provided. Integrable many-body systems generalizing the rational Calogero model arise in the representation in terms of eigenvalues. Each element of $W_{1+\infty}$ algebra gives rise to KP/Toda $蟿$-functions. The hidden symmetry given by the families of commuting Hamiltonians is in charge of the special, (skew) hypergeometric $蟿$-functions among these. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.06623v3-abstract-full').style.display = 'none'; document.getElementById('2306.06623v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">43 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-09/23; IITP/TH-09/23; ITEP/TH-13/23; MIPT/TH-10/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 09 (2023) 65 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.12282">arXiv:2305.12282</a> <span> [<a href="https://arxiv.org/pdf/2305.12282">pdf</a>, <a href="https://arxiv.org/ps/2305.12282">ps</a>, <a href="https://arxiv.org/format/2305.12282">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP11(2023)165">10.1007/JHEP11(2023)165 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> 3-Schurs from explicit representation of Yangian $Y(\hat{\mathfrak{gl}}_1)$. Levels 1-5 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">N. Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.12282v1-abstract-short" style="display: inline;"> We suggest an ansatz for representation of affine Yangian $Y(\hat{ \mathfrak{gl}}_1)$ by differential operators in the triangular set of time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates the MacMahon formula for the number of $3d$ Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of com… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.12282v1-abstract-full').style.display = 'inline'; document.getElementById('2305.12282v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.12282v1-abstract-full" style="display: none;"> We suggest an ansatz for representation of affine Yangian $Y(\hat{ \mathfrak{gl}}_1)$ by differential operators in the triangular set of time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates the MacMahon formula for the number of $3d$ Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of commuting "cut-and-join" generators $蠄_n$ of the Yangian. We manage to push this tedious program through to the 3-Schur polynomials of level 5, and this provides a rather big sample set, which can be now investigated by other methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.12282v1-abstract-full').style.display = 'none'; document.getElementById('2305.12282v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.00197">arXiv:2304.00197</a> <span> [<a href="https://arxiv.org/pdf/2304.00197">pdf</a>, <a href="https://arxiv.org/ps/2304.00197">ps</a>, <a href="https://arxiv.org/format/2304.00197">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0217732324500251">10.1142/S0217732324500251 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On information paradox and the fate of black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.00197v1-abstract-short" style="display: inline;"> A sketchy review of the "island" paradigm in black hole evaporation theory, which actually brings us back to the old idea that interior of black hole decouples from our universe after Page time, so that Hawking radiation is entangled with emerging new universe, thus leaving no room for the information paradox. Instead this provides a self-consistent description of multiverse, where every black hol… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.00197v1-abstract-full').style.display = 'inline'; document.getElementById('2304.00197v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.00197v1-abstract-full" style="display: none;"> A sketchy review of the "island" paradigm in black hole evaporation theory, which actually brings us back to the old idea that interior of black hole decouples from our universe after Page time, so that Hawking radiation is entangled with emerging new universe, thus leaving no room for the information paradox. Instead this provides a self-consistent description of multiverse, where every black hole in a parent universe is a white hole -- the origin -- of a new one. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.00197v1-abstract-full').style.display = 'none'; document.getElementById('2304.00197v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> MPLA 39 (2024) 2450025 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.08851">arXiv:2303.08851</a> <span> [<a href="https://arxiv.org/pdf/2303.08851">pdf</a>, <a href="https://arxiv.org/ps/2303.08851">ps</a>, <a href="https://arxiv.org/format/2303.08851">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2023.116245">10.1016/j.nuclphysb.2023.116245 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Position Space Equations for Banana Feynman Diagrams </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">Victor Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Alexei Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Suprun%2C+P">Pavel Suprun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.08851v1-abstract-short" style="display: inline;"> The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties. We study these equations in the simplest example of banana diagrams. They contain any number of loops, but can be efficiently handled in position rather than mom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08851v1-abstract-full').style.display = 'inline'; document.getElementById('2303.08851v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.08851v1-abstract-full" style="display: none;"> The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties. We study these equations in the simplest example of banana diagrams. They contain any number of loops, but can be efficiently handled in position rather than momentum representation, where loop integrals do not show up. We derive equations for the case of scalar fields, explain their origins and drastic simplification at coincident masses. To further simplify the story we do not consider coincident points, i.e. ignore delta-function contributions and ultraviolet divergences for the most part. The equations in this case reduce to homogeneous and have as many solutions as there are different Green functions -- $2^n$ for $n$ loops in quadratic theory, what reduces to just $n+1$ for coincident masses, i.e. for a single field. We comment on the recovery of the delta-functions directly from the homogeneous equations and also compare our result with momentum space formulas known in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08851v1-abstract-full').style.display = 'none'; document.getElementById('2303.08851v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-09/23, FIAN/TH-07/23, ITEP/TH-10/23, IITP/TH-08/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.B 992 (2023) 116245 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.05273">arXiv:2303.05273</a> <span> [<a href="https://arxiv.org/pdf/2303.05273">pdf</a>, <a href="https://arxiv.org/format/2303.05273">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2023.137964">10.1016/j.physletb.2023.137964 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Many-body integrable systems implied by WLZZ models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.05273v1-abstract-short" style="display: inline;"> We provide some details about the recently discovered integrable systems implied by commutativity of $W$ operators along the rays on the plane of roots of $w_\infty$-algebra. The simplest system of this type is the rational Calogero model, other systems escaped attention in the past. Existence of these systems is intimately tied to the very interesting WLZZ matrix models, which are now under inten… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.05273v1-abstract-full').style.display = 'inline'; document.getElementById('2303.05273v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.05273v1-abstract-full" style="display: none;"> We provide some details about the recently discovered integrable systems implied by commutativity of $W$ operators along the rays on the plane of roots of $w_\infty$-algebra. The simplest system of this type is the rational Calogero model, other systems escaped attention in the past. Existence of these systems is intimately tied to the very interesting WLZZ matrix models, which are now under intensive study. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.05273v1-abstract-full').style.display = 'none'; document.getElementById('2303.05273v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-07/23; FIAN/TD-06/23; ITEP/TH-08/23; IITP/TH-06/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Letters B842 (2023) 137964 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.00552">arXiv:2303.00552</a> <span> [<a href="https://arxiv.org/pdf/2303.00552">pdf</a>, <a href="https://arxiv.org/format/2303.00552">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2023.116283">10.1016/j.nuclphysb.2023.116283 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> $(q,t)$-deformed (skew) Hurwitz $蟿$-functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Liu%2C+F">Fan Liu</a>, <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Wang%2C+R">Rui Wang</a>, <a href="/search/hep-th?searchtype=author&query=Zhao%2C+W">Wei-Zhong Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.00552v2-abstract-short" style="display: inline;"> We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a $(q,t)$-deformation of the earlier studied models. As before, a key role is played by an appropriate deformation of the cut-and-join rotation operator. We out… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00552v2-abstract-full').style.display = 'inline'; document.getElementById('2303.00552v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.00552v2-abstract-full" style="display: none;"> We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a $(q,t)$-deformation of the earlier studied models. As before, a key role is played by an appropriate deformation of the cut-and-join rotation operator. We outline its expression both in terms of generators of the quantum toroidal algebra and in terms of the Macdonald difference operators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.00552v2-abstract-full').style.display = 'none'; document.getElementById('2303.00552v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-05/23; IITP/TH-03/23; ITEP/TH-03/23; MIPT/TH-03/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys. B993 (2023) 116283 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.05903">arXiv:2302.05903</a> <span> [<a href="https://arxiv.org/pdf/2302.05903">pdf</a>, <a href="https://arxiv.org/format/2302.05903">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2023.138037">10.1016/j.physletb.2023.138037 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Averaging method in combinatorics of symmetric polynomials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.05903v2-abstract-short" style="display: inline;"> We elaborate on the recent suggestion to consider averaging of Cauchy identities for the Schur functions over power sum variables. This procedure has apparent parallels with the Borel transform, only it changes the number of combinatorial factors like $d_R$ in the sums over Young diagrams instead of just factorials in ordinary sums over numbers. It provides a universal view on a number of previous… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.05903v2-abstract-full').style.display = 'inline'; document.getElementById('2302.05903v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.05903v2-abstract-full" style="display: none;"> We elaborate on the recent suggestion to consider averaging of Cauchy identities for the Schur functions over power sum variables. This procedure has apparent parallels with the Borel transform, only it changes the number of combinatorial factors like $d_R$ in the sums over Young diagrams instead of just factorials in ordinary sums over numbers. It provides a universal view on a number of previously known, but seemingly random identities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.05903v2-abstract-full').style.display = 'none'; document.getElementById('2302.05903v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-06/22; FIAN/TD-03/22; ITEP/TH-06/22; IITP/TH-05/22 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett. B843 (2023) 138037 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2301.11877">arXiv:2301.11877</a> <span> [<a href="https://arxiv.org/pdf/2301.11877">pdf</a>, <a href="https://arxiv.org/ps/2301.11877">ps</a>, <a href="https://arxiv.org/format/2301.11877">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2023.137805">10.1016/j.physletb.2023.137805 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On KP-integrable skew Hurwitz $蟿$-functions and their $尾$-deformations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Zhao%2C+W">Wei-Zhong Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2301.11877v2-abstract-short" style="display: inline;"> We extend the old formalism of cut-and-join operators in the theory of Hurwitz $蟿$-functions to description of a wide family of KP-integrable {\it skew} Hurwitz $蟿$-functions, which include, in particular, the newly discovered interpolating WLZZ models. Recently, the simplest of them was related to a superintegrable two-matrix model with two potentials and one external matrix field. Now we provide… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.11877v2-abstract-full').style.display = 'inline'; document.getElementById('2301.11877v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2301.11877v2-abstract-full" style="display: none;"> We extend the old formalism of cut-and-join operators in the theory of Hurwitz $蟿$-functions to description of a wide family of KP-integrable {\it skew} Hurwitz $蟿$-functions, which include, in particular, the newly discovered interpolating WLZZ models. Recently, the simplest of them was related to a superintegrable two-matrix model with two potentials and one external matrix field. Now we provide detailed proofs, and a generalization to a multi-matrix representation, and propose the $尾$ deformation of the matrix model as well. The general interpolating WLZZ model is generated by a $W$-representation given by a sum of operators from a one-parametric commutative sub-family (a commutative subalgebra of $w_\infty$). Different commutative families are related by cut-and-join rotations. Two of these sub-families (`vertical' and `45-degree') turn out to be nothing but the trigonometric and rational Calogero-Sutherland Hamiltonians, the `horizontal' family is represented by simple derivatives. Other families require an additional analysis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.11877v2-abstract-full').style.display = 'none'; document.getElementById('2301.11877v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, LaTeX</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-02/23; IITP/TH-02/23; ITEP/TH-02/23; MIPT/TH-02/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Letters B839 (2023) 137805 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2301.04107">arXiv:2301.04107</a> <span> [<a href="https://arxiv.org/pdf/2301.04107">pdf</a>, <a href="https://arxiv.org/format/2301.04107">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epjc/s10052-023-11549-0">10.1140/epjc/s10052-023-11549-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Interpolating Matrix Models for WLZZ series </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Mishnyakov%2C+V">V. Mishnyakov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Popolitov%2C+A">A. Popolitov</a>, <a href="/search/hep-th?searchtype=author&query=Wang%2C+R">Rui Wang</a>, <a href="/search/hep-th?searchtype=author&query=Zhao%2C+W">Wei-Zhong Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2301.04107v2-abstract-short" style="display: inline;"> We suggest a two-matrix model depending on three (infinite) sets of parameters which interpolates between all the models proposed in arXiv:2206.13038, and defined there through $W$-representations. We also discuss further generalizations of these WLZZ models realized by $W$-representations associated with infinite commutative families of generators of $w_\infty$-algebra which are presumably relate… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.04107v2-abstract-full').style.display = 'inline'; document.getElementById('2301.04107v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2301.04107v2-abstract-full" style="display: none;"> We suggest a two-matrix model depending on three (infinite) sets of parameters which interpolates between all the models proposed in arXiv:2206.13038, and defined there through $W$-representations. We also discuss further generalizations of these WLZZ models realized by $W$-representations associated with infinite commutative families of generators of $w_\infty$-algebra which are presumably related to more sophisticated multi-matrix models. Integrable properties of these generalizations are described by what we call the skew hypergeometric $蟿$-functions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.04107v2-abstract-full').style.display = 'none'; document.getElementById('2301.04107v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FIAN/TD-01/23; IITP/TH-01/23; ITEP/TH-01/23; MIPT/TH-01/23 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Eur. Phys. J. C 83 (2023) 377 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.04859">arXiv:2212.04859</a> <span> [<a href="https://arxiv.org/pdf/2212.04859">pdf</a>, <a href="https://arxiv.org/ps/2212.04859">ps</a>, <a href="https://arxiv.org/format/2212.04859">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epjc/s10052-023-11398-x">10.1140/epjc/s10052-023-11398-x <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Equating Schur Functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.04859v1-abstract-short" style="display: inline;"> We wonder if there is a way to make all Schur functions in all representations equal. This is impossible for fixed value of time variables, but can be achieved for averages. It appears that the corresponding measure is just Gaussian in times, which are all independent. The generating function for the number of Young diagrams does not straightforwardly appear as a product, but is reproduced in a no… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.04859v1-abstract-full').style.display = 'inline'; document.getElementById('2212.04859v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.04859v1-abstract-full" style="display: none;"> We wonder if there is a way to make all Schur functions in all representations equal. This is impossible for fixed value of time variables, but can be achieved for averages. It appears that the corresponding measure is just Gaussian in times, which are all independent. The generating function for the number of Young diagrams does not straightforwardly appear as a product, but is reproduced in a non-trivial way. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.04859v1-abstract-full').style.display = 'none'; document.getElementById('2212.04859v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.02632">arXiv:2212.02632</a> <span> [<a href="https://arxiv.org/pdf/2212.02632">pdf</a>, <a href="https://arxiv.org/ps/2212.02632">ps</a>, <a href="https://arxiv.org/format/2212.02632">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/B978-0-323-95703-8.00040-9">10.1016/B978-0-323-95703-8.00040-9 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Integrability and Matrix Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.02632v1-abstract-short" style="display: inline;"> A brief review of the eigenvalue matrix model integrability and superintegrability properties, focused on the simplest, still representative, Gaussian Hermitian case. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.02632v1-abstract-full" style="display: none;"> A brief review of the eigenvalue matrix model integrability and superintegrability properties, focused on the simplest, still representative, Gaussian Hermitian case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.02632v1-abstract-full').style.display = 'none'; document.getElementById('2212.02632v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Enc Math Phys 2024 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.01289">arXiv:2212.01289</a> <span> [<a href="https://arxiv.org/pdf/2212.01289">pdf</a>, <a href="https://arxiv.org/format/2212.01289">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1134/S0021364022603207">10.1134/S0021364022603207 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Multistrand Eigenvalue conjecture and Racah symmetries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">Andrey Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.01289v1-abstract-short" style="display: inline;"> Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with $\mathcal{R}$-matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue conjecture. In this paper we study symmetries of Racah matrices which follow from the eigenvalue conjecture for multistrand braids. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.01289v1-abstract-full" style="display: none;"> Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with $\mathcal{R}$-matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue conjecture. In this paper we study symmetries of Racah matrices which follow from the eigenvalue conjecture for multistrand braids. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.01289v1-abstract-full').style.display = 'none'; document.getElementById('2212.01289v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ITEP/TH-26/22 IITP/TH-23/22 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.14956">arXiv:2211.14956</a> <span> [<a href="https://arxiv.org/pdf/2211.14956">pdf</a>, <a href="https://arxiv.org/ps/2211.14956">ps</a>, <a href="https://arxiv.org/format/2211.14956">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2023.137887">10.1016/j.physletb.2023.137887 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hunt for 3-Schur polynomials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a>, <a href="/search/hep-th?searchtype=author&query=Tselousov%2C+N">N. Tselousov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2211.14956v2-abstract-short" style="display: inline;"> This paper describes our attempt to understand the recent success of Na Wang in constructing the 3-Schur polynomials, associated with the plane partitions. We provide a rather detailed review and try to figure out the new insights, which allowed to overcome the problems of the previous efforts. In result we provide a very simple definition of time-variables ${\bf P}_{i\geqslant j}$ and the cut-and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.14956v2-abstract-full').style.display = 'inline'; document.getElementById('2211.14956v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.14956v2-abstract-full" style="display: none;"> This paper describes our attempt to understand the recent success of Na Wang in constructing the 3-Schur polynomials, associated with the plane partitions. We provide a rather detailed review and try to figure out the new insights, which allowed to overcome the problems of the previous efforts. In result we provide a very simple definition of time-variables ${\bf P}_{i\geqslant j}$ and the cut-and-join operator $\hat W_2$, which generates the set of $3$-Schur functions. Some coefficients in $\hat W_2$ remain undefined and require more effort to be fixed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.14956v2-abstract-full').style.display = 'none'; document.getElementById('2211.14956v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.09993">arXiv:2210.09993</a> <span> [<a href="https://arxiv.org/pdf/2210.09993">pdf</a>, <a href="https://arxiv.org/format/2210.09993">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP03(2023)116">10.1007/JHEP03(2023)116 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spectral curves and $W$-representations of matrix models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Mironov%2C+A">A. Mironov</a>, <a href="/search/hep-th?searchtype=author&query=Morozov%2C+A">A. Morozov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.09993v3-abstract-short" style="display: inline;"> We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.09993v3-abstract-full').style.display = 'inline'; document.getElementById('2210.09993v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.09993v3-abstract-full" style="display: none;"> We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter $n$, when the model depends on additional couplings (dual times). In this case, the relation between topological and $1/N$ expansions is broken. On the other hand, all the WLZZ partition functions are $蟿$-functions of the Toda lattice hierarchy, and these models also celebrate the superintegrability properties. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.09993v3-abstract-full').style.display = 'none'; document.getElementById('2210.09993v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MIPT/TH-18/22; FIAN/TD-13/22; ITEP/TH-21/22; IITP/TH-20/22 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. High Energ. Phys. 2023 (2023) 116 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.08058">arXiv:2209.08058</a> <span> [<a href="https://arxiv.org/pdf/2209.08058">pdf</a>, <a href="https://arxiv.org/format/2209.08058">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Nuclear Experiment">nucl-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.130.202301">10.1103/PhysRevLett.130.202301 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Beam Energy Dependence of Triton Production and Yield Ratio ($\mathrm{N}_t \times \mathrm{N}_p/\mathrm{N}_d^2$) in Au+Au Collisions at RHIC </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=STAR+Collaboration"> STAR Collaboration</a>, <a href="/search/hep-th?searchtype=author&query=Abdulhamid%2C+M+I">M. I. Abdulhamid</a>, <a href="/search/hep-th?searchtype=author&query=Aboona%2C+B+E">B. E. Aboona</a>, <a href="/search/hep-th?searchtype=author&query=Adam%2C+J">J. Adam</a>, <a href="/search/hep-th?searchtype=author&query=Adams%2C+J+R">J. R. Adams</a>, <a href="/search/hep-th?searchtype=author&query=Agakishiev%2C+G">G. Agakishiev</a>, <a href="/search/hep-th?searchtype=author&query=Aggarwal%2C+I">I. Aggarwal</a>, <a href="/search/hep-th?searchtype=author&query=Aggarwal%2C+M+M">M. M. Aggarwal</a>, <a href="/search/hep-th?searchtype=author&query=Ahammed%2C+Z">Z. Ahammed</a>, <a href="/search/hep-th?searchtype=author&query=Aitbaev%2C+A">A. Aitbaev</a>, <a href="/search/hep-th?searchtype=author&query=Alekseev%2C+I">I. Alekseev</a>, <a href="/search/hep-th?searchtype=author&query=Anderson%2C+D+M">D. M. Anderson</a>, <a href="/search/hep-th?searchtype=author&query=Aparin%2C+A">A. Aparin</a>, <a href="/search/hep-th?searchtype=author&query=Aslam%2C+S">S. Aslam</a>, <a href="/search/hep-th?searchtype=author&query=Atchison%2C+J">J. Atchison</a>, <a href="/search/hep-th?searchtype=author&query=Averichev%2C+G+S">G. S. Averichev</a>, <a href="/search/hep-th?searchtype=author&query=Bairathi%2C+V">V. Bairathi</a>, <a href="/search/hep-th?searchtype=author&query=Baker%2C+W">W. Baker</a>, <a href="/search/hep-th?searchtype=author&query=Cap%2C+J+G+B">J. G. Ball Cap</a>, <a href="/search/hep-th?searchtype=author&query=Barish%2C+K">K. Barish</a>, <a href="/search/hep-th?searchtype=author&query=Bhagat%2C+P">P. Bhagat</a>, <a href="/search/hep-th?searchtype=author&query=Bhasin%2C+A">A. Bhasin</a>, <a href="/search/hep-th?searchtype=author&query=Bhatta%2C+S">S. Bhatta</a>, <a href="/search/hep-th?searchtype=author&query=Bordyuzhin%2C+I+G">I. G. Bordyuzhin</a>, <a href="/search/hep-th?searchtype=author&query=Brandenburg%2C+J+D">J. D. Brandenburg</a> , et al. (333 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.08058v2-abstract-short" style="display: inline;"> We report the triton ($t$) production in mid-rapidity ($|y| <$ 0.5) Au+Au collisions at $\sqrt{s_\mathrm{NN}}$= 7.7--200 GeV measured by the STAR experiment from the first phase of the beam energy scan at the Relativistic Heavy Ion Collider (RHIC). The nuclear compound yield ratio ($\mathrm{N}_t \times \mathrm{N}_p/\mathrm{N}_d^2$), which is predicted to be sensitive to the fluctuation of local ne… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08058v2-abstract-full').style.display = 'inline'; document.getElementById('2209.08058v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.08058v2-abstract-full" style="display: none;"> We report the triton ($t$) production in mid-rapidity ($|y| <$ 0.5) Au+Au collisions at $\sqrt{s_\mathrm{NN}}$= 7.7--200 GeV measured by the STAR experiment from the first phase of the beam energy scan at the Relativistic Heavy Ion Collider (RHIC). The nuclear compound yield ratio ($\mathrm{N}_t \times \mathrm{N}_p/\mathrm{N}_d^2$), which is predicted to be sensitive to the fluctuation of local neutron density, is observed to decrease monotonically with increasing charged-particle multiplicity ($dN_{ch}/d畏$) and follows a scaling behavior. The $dN_{ch}/d畏$ dependence of the yield ratio is compared to calculations from coalescence and thermal models. Enhancements in the yield ratios relative to the coalescence baseline are observed in the 0\%-10\% most central collisions at 19.6 and 27 GeV, with a significance of 2.3$蟽$ and 3.4$蟽$, respectively, giving a combined significance of 4.1$蟽$. The enhancements are not observed in peripheral collisions or model calculations without critical fluctuation, and decreases with a smaller $p_{T}$ acceptance. The physics implications of these results on the QCD phase structure and the production mechanism of light nuclei in heavy-ion collisions are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08058v2-abstract-full').style.display = 'none'; document.getElementById('2209.08058v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 4 figures, Supplemental Material: http://link.aps.org/supplemental/10.1103/PhysRevLett.130.202301</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 130, 202301 (2023) </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> <li> <a href="/search/?searchtype=author&query=Morozov%2C+A&start=150" class="pagination-link " aria-label="Page 4" aria-current="page">4 </a> </li> <li> <a 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