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</div> <div class="control"> <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=Galajinsky%2C+A&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Galajinsky%2C+A&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Galajinsky%2C+A&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </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/2411.13928">arXiv:2411.13928</a> <span> [<a href="https://arxiv.org/pdf/2411.13928">pdf</a>, <a href="https://arxiv.org/format/2411.13928">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="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> </div> <p class="title is-5 mathjax"> Rational Ruijsenaars-Schneider model with cosmological constant </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2411.13928v1-abstract-short" style="display: inline;"> The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincare algebra in 1+1 dimensions to the anti de Sitter algebra is studied. It is s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.13928v1-abstract-full').style.display = 'inline'; document.getElementById('2411.13928v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.13928v1-abstract-full" style="display: none;"> The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincare algebra in 1+1 dimensions to the anti de Sitter algebra is studied. It is shown that amendments including a cosmological constant are feasible for the rational variant, while the hyperbolic and trigonometric systems are ruled out by our analysis. The issue of integrability of the deformed rational model is discussed in some detail. A complete proof of integrability remains a challenge. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.13928v1-abstract-full').style.display = 'none'; document.getElementById('2411.13928v1-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">14 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/2403.09204">arXiv:2403.09204</a> <span> [<a href="https://arxiv.org/pdf/2403.09204">pdf</a>, <a href="https://arxiv.org/format/2403.09204">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</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"> Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2403.09204v2-abstract-short" style="display: inline;"> Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09204v2-abstract-full').style.display = 'inline'; document.getElementById('2403.09204v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.09204v2-abstract-full" style="display: none;"> Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09204v2-abstract-full').style.display = 'none'; document.getElementById('2403.09204v2-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 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 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">V2: 19 pages, concluding part extended, refs. added, the version to appear in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.04084">arXiv:2312.04084</a> <span> [<a href="https://arxiv.org/pdf/2312.04084">pdf</a>, <a href="https://arxiv.org/format/2312.04084">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"> Equations of fluid mechanics with N=1 Schrodinger supersymmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2312.04084v1-abstract-short" style="display: inline;"> Equations of fluid mechanics with N=1 Schrodinger supersymmetry are formulated within the method of nonlinear realizations of Lie groups. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.04084v1-abstract-full" style="display: none;"> Equations of fluid mechanics with N=1 Schrodinger supersymmetry are formulated within the method of nonlinear realizations of Lie groups. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.04084v1-abstract-full').style.display = 'none'; document.getElementById('2312.04084v1-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 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">11 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/2309.13891">arXiv:2309.13891</a> <span> [<a href="https://arxiv.org/pdf/2309.13891">pdf</a>, <a href="https://arxiv.org/format/2309.13891">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</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"> Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2309.13891v1-abstract-short" style="display: inline;"> An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their algebraic resolvability is proven. The supersymmetric generalization is used to build a novel integrable isospin extension of the Ruijsenaars-Schneider three-body sy… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.13891v1-abstract-full').style.display = 'inline'; document.getElementById('2309.13891v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.13891v1-abstract-full" style="display: none;"> An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their algebraic resolvability is proven. The supersymmetric generalization is used to build a novel integrable isospin extension of the Ruijsenaars-Schneider three-body system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.13891v1-abstract-full').style.display = 'none'; document.getElementById('2309.13891v1-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 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">16 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/2302.00317">arXiv:2302.00317</a> <span> [<a href="https://arxiv.org/pdf/2302.00317">pdf</a>, <a href="https://arxiv.org/format/2302.00317">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.2023.138042">10.1016/j.physletb.2023.138042 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Remarks on higher Schwarzians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2302.00317v2-abstract-short" style="display: inline;"> The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev-Ye-Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to Aharonov, Bertilsson, and Schippers. Physical applications of the higher Schwarzian derivatives have not yet been discussed in any detail. In this work, we link Be… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.00317v2-abstract-full').style.display = 'inline'; document.getElementById('2302.00317v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.00317v2-abstract-full" style="display: none;"> The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev-Ye-Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to Aharonov, Bertilsson, and Schippers. Physical applications of the higher Schwarzian derivatives have not yet been discussed in any detail. In this work, we link Bertilsson's variant to the l-conformal Galilei group, as well as discuss some of its interesting peculiarities. These include a recurrence relation, which allows one to construct the higher Schwarzians iteratively, a composition law, and symmetry transformations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.00317v2-abstract-full').style.display = 'none'; document.getElementById('2302.00317v2-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> 16 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 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">V2: 12 pages, minor improvements, the version submitted for publication</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.14544">arXiv:2210.14544</a> <span> [<a href="https://arxiv.org/pdf/2210.14544">pdf</a>, <a href="https://arxiv.org/format/2210.14544">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/10.1103/PhysRevD.107.026008">10.1103/PhysRevD.107.026008 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The group-theoretic approach to perfect fluid equations with conformal symmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2210.14544v2-abstract-short" style="display: inline;"> The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and limitations of the method, which is here applied to construct perfect fluid equations with conformal symmetry. Four cases are studied in detail, which include t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.14544v2-abstract-full').style.display = 'inline'; document.getElementById('2210.14544v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.14544v2-abstract-full" style="display: none;"> The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and limitations of the method, which is here applied to construct perfect fluid equations with conformal symmetry. Four cases are studied in detail, which include the Schrodinger group, the l-conformal Galilei group, the Lifshitz group, and the relativistic conformal group. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.14544v2-abstract-full').style.display = 'none'; document.getElementById('2210.14544v2-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> 8 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 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">v2: 23 pages, the introductory and concluding parts extended, acknowledgement and references added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.12576">arXiv:2205.12576</a> <span> [<a href="https://arxiv.org/pdf/2205.12576">pdf</a>, <a href="https://arxiv.org/ps/2205.12576">ps</a>, <a href="https://arxiv.org/format/2205.12576">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="Fluid Dynamics">physics.flu-dyn</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.2022.115965">10.1016/j.nuclphysb.2022.115965 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Equations of fluid dynamics with the l-conformal Galilei symmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2205.12576v1-abstract-short" style="display: inline;"> Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a suitable modification of the conventional equation of state. Conserved charges associated with the l-conformal Galilei symmetry transformations are presented. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.12576v1-abstract-full" style="display: none;"> Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a suitable modification of the conventional equation of state. Conserved charges associated with the l-conformal Galilei symmetry transformations are presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.12576v1-abstract-full').style.display = 'none'; document.getElementById('2205.12576v1-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 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">14 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/2203.00273">arXiv:2203.00273</a> <span> [<a href="https://arxiv.org/pdf/2203.00273">pdf</a>, <a href="https://arxiv.org/format/2203.00273">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="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.2022.137119">10.1016/j.physletb.2022.137119 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Generalised point vortices on a plane </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2203.00273v1-abstract-short" style="display: inline;"> A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. It… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.00273v1-abstract-full').style.display = 'inline'; document.getElementById('2203.00273v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.00273v1-abstract-full" style="display: none;"> A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. It is emphasised that the n-vortex planar model and plenty of its generalisations enjoy the nonrelativistic scale invariance, which gives room for possible holographic applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.00273v1-abstract-full').style.display = 'none'; document.getElementById('2203.00273v1-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, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">11 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/2201.10187">arXiv:2201.10187</a> <span> [<a href="https://arxiv.org/pdf/2201.10187">pdf</a>, <a href="https://arxiv.org/format/2201.10187">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="General Relativity and Quantum Cosmology">gr-qc</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/10.1103/PhysRevD.105.106023">10.1103/PhysRevD.105.106023 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamical realizations of the Lifshitz group </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2201.10187v3-abstract-short" style="display: inline;"> Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the Ermakov-Milne-Pinney equation is proposed. Invariant derivative and field combinations are introduced, which enable one to construct a plethora of dynamical sys… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.10187v3-abstract-full').style.display = 'inline'; document.getElementById('2201.10187v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.10187v3-abstract-full" style="display: none;"> Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the Ermakov-Milne-Pinney equation is proposed. Invariant derivative and field combinations are introduced, which enable one to construct a plethora of dynamical systems enjoying the Lifshitz symmetry. A metric of the Lorentzian signature in (d+2)-dimensional spacetime and the energy-momentum tensor are constructed, which lead to the generalized Ermakov-Milne-Pinney equation upon imposing the Einstein equations. The method of nonlinear realizations is used for building Lorentzian metrics with the Lifshitz isometry group. In particular, a (2d+2)-dimensional metric is constructed, which enjoys an extra invariance under the Galilei boosts. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.10187v3-abstract-full').style.display = 'none'; document.getElementById('2201.10187v3-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> 17 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">v3: presentation in sect. 2 and sect. 5 improved, one reference added; the version accepted for publication in Phys. Rev. D</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.06083">arXiv:2111.06083</a> <span> [<a href="https://arxiv.org/pdf/2111.06083">pdf</a>, <a href="https://arxiv.org/format/2111.06083">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="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.nuclphysb.2022.115668">10.1016/j.nuclphysb.2022.115668 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Remarks on N=1 supersymmetric extension of the Euler top </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2111.06083v1-abstract-short" style="display: inline;"> A natural N=1 supersymmetric extension of the Euler top, which introduces exactly one fermionic counterpart for each bosonic degree of freedom, is considered. The equations of motion, their symmetries and integrals of motion are given. It is demonstrated that, although in general the system lacks the integrability property, it admits an interesting integrable reduction, for which all fermions are… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.06083v1-abstract-full').style.display = 'inline'; document.getElementById('2111.06083v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.06083v1-abstract-full" style="display: none;"> A natural N=1 supersymmetric extension of the Euler top, which introduces exactly one fermionic counterpart for each bosonic degree of freedom, is considered. The equations of motion, their symmetries and integrals of motion are given. It is demonstrated that, although in general the system lacks the integrability property, it admits an interesting integrable reduction, for which all fermions are proportional to one and the same Grassmann-odd number - a value of the conserved supercharge. A generalisation involving an arbitrary three-dimensional real Lie algebra is proposed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.06083v1-abstract-full').style.display = 'none'; document.getElementById('2111.06083v1-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 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </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</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.09335">arXiv:2106.09335</a> <span> [<a href="https://arxiv.org/pdf/2106.09335">pdf</a>, <a href="https://arxiv.org/ps/2106.09335">ps</a>, <a href="https://arxiv.org/format/2106.09335">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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="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.2021.136483">10.1016/j.physletb.2021.136483 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Some metrics admitting nonpolynomial first integrals of the geodesic equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2106.09335v2-abstract-short" style="display: inline;"> It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.09335v2-abstract-full" style="display: none;"> It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.09335v2-abstract-full').style.display = 'none'; document.getElementById('2106.09335v2-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 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </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">V2: 14 pages, minor improvements, the version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2105.14808">arXiv:2105.14808</a> <span> [<a href="https://arxiv.org/pdf/2105.14808">pdf</a>, <a href="https://arxiv.org/format/2105.14808">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/10.1007/JHEP08(2021)165">10.1007/JHEP08(2021)165 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=1,2,3 l-conformal Galilei superalgebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="2105.14808v2-abstract-short" style="display: inline;"> The issue of constructing N=1,2,3 supersymmetric extensions of the l-conformal Galilei algebra is reconsidered following the approach in [JHEP 1709 (2017) 131]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d=1, N-extended superconformal group, a new N=1 l-conformal Galilei superalgebra, two new N=2 variants, and two new N=3 version… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.14808v2-abstract-full').style.display = 'inline'; document.getElementById('2105.14808v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2105.14808v2-abstract-full" style="display: none;"> The issue of constructing N=1,2,3 supersymmetric extensions of the l-conformal Galilei algebra is reconsidered following the approach in [JHEP 1709 (2017) 131]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d=1, N-extended superconformal group, a new N=1 l-conformal Galilei superalgebra, two new N=2 variants, and two new N=3 versions are built. Realisations in terms of differential operators in superspace are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.14808v2-abstract-full').style.display = 'none'; document.getElementById('2105.14808v2-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, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2021. </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">v2: 17 pages, introductory and concluding parts extended, references added; the version accepted in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.12426">arXiv:2103.12426</a> <span> [<a href="https://arxiv.org/pdf/2103.12426">pdf</a>, <a href="https://arxiv.org/format/2103.12426">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/10.1103/PhysRevD.103.126007">10.1103/PhysRevD.103.126007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Remarks on D(2,1;a) super-Schwarzian derivative </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="2103.12426v1-abstract-short" style="display: inline;"> It was recently demonstrated that N=1,2,3,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realisations to finite-dimensional superconformal groups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2), respectively, thus avoiding the use of superconformal field theory techniques. In this work, a similar construction is applied to the exceptional supergroup D(2,1;a), which… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.12426v1-abstract-full').style.display = 'inline'; document.getElementById('2103.12426v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.12426v1-abstract-full" style="display: none;"> It was recently demonstrated that N=1,2,3,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realisations to finite-dimensional superconformal groups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2), respectively, thus avoiding the use of superconformal field theory techniques. In this work, a similar construction is applied to the exceptional supergroup D(2,1;a), which describes the most general N=4 supersymmetric extension of SL(2,R), with the aim to study possible candidates for a D(2,1;a) super-Schwarzian derivative. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.12426v1-abstract-full').style.display = 'none'; document.getElementById('2103.12426v1-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> 23 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </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">23 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 126007 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2012.01054">arXiv:2012.01054</a> <span> [<a href="https://arxiv.org/pdf/2012.01054">pdf</a>, <a href="https://arxiv.org/ps/2012.01054">ps</a>, <a href="https://arxiv.org/format/2012.01054">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="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/10.1140/epjc/s10052-021-08993-1">10.1140/epjc/s10052-021-08993-1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spinning particles on 2-sphere in accord with the Bianchi classification </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2012.01054v1-abstract-short" style="display: inline;"> Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector obeying the structure relations of a 3d real Lie algebra. Generalisations involving an external field of the Dirac monopole, or the motion on the group manifol… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.01054v1-abstract-full').style.display = 'inline'; document.getElementById('2012.01054v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2012.01054v1-abstract-full" style="display: none;"> Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector obeying the structure relations of a 3d real Lie algebra. Generalisations involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar extensions, which rely upon d=4,5,6 real Lie algebras, is elucidated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.01054v1-abstract-full').style.display = 'none'; document.getElementById('2012.01054v1-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, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2020. </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> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.13064">arXiv:2009.13064</a> <span> [<a href="https://arxiv.org/pdf/2009.13064">pdf</a>, <a href="https://arxiv.org/format/2009.13064">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.2020.135885">10.1016/j.physletb.2020.135885 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=3 super-Schwarzian from OSp(3|2) invariants </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2009.13064v2-abstract-short" style="display: inline;"> It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2), respectively. In this work, a similar scheme is realised for OSp(3|2). It is shown that the N=3 case exhibits a surprisingly richer structure of invariants, the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.13064v2-abstract-full').style.display = 'inline'; document.getElementById('2009.13064v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.13064v2-abstract-full" style="display: none;"> It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2), respectively. In this work, a similar scheme is realised for OSp(3|2). It is shown that the N=3 case exhibits a surprisingly richer structure of invariants, the N=3 super-Schwarzian being a particular member. We suggest that the extra invariants may prove useful in building an N=3 supersymmetric extension of the Sachdev-Ye-Kitaev model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.13064v2-abstract-full').style.display = 'none'; document.getElementById('2009.13064v2-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 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </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">V2: 10 pages, a typo fixed in the abstract and main text; the version to appear in PLB. arXiv admin note: text overlap with arXiv:2007.04015</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.04015">arXiv:2007.04015</a> <span> [<a href="https://arxiv.org/pdf/2007.04015">pdf</a>, <a href="https://arxiv.org/ps/2007.04015">ps</a>, <a href="https://arxiv.org/format/2007.04015">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/10.1103/PhysRevD.102.106015">10.1103/PhysRevD.102.106015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=4 super-Schwarzian via nonlinear realizations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Krivonos%2C+S">Sergey Krivonos</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="2007.04015v2-abstract-short" style="display: inline;"> Current studies of supersymmetric extensions of the Sachdev-Ye-Kitaev model stimulate a renewed interest in super-Schwarzian derivatives. In this work, we apply the method of nonlinear realizations to the finite-dimensional superconformal group SU(1,1|2) and link its invariants to the N=4 super-Schwarzian. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.04015v2-abstract-full" style="display: none;"> Current studies of supersymmetric extensions of the Sachdev-Ye-Kitaev model stimulate a renewed interest in super-Schwarzian derivatives. In this work, we apply the method of nonlinear realizations to the finite-dimensional superconformal group SU(1,1|2) and link its invariants to the N=4 super-Schwarzian. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.04015v2-abstract-full').style.display = 'none'; document.getElementById('2007.04015v2-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 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </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">V2: minor improvements; the version to appear in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 102, 106015 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.04489">arXiv:2004.04489</a> <span> [<a href="https://arxiv.org/pdf/2004.04489">pdf</a>, <a href="https://arxiv.org/format/2004.04489">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/10.1007/JHEP06(2020)027">10.1007/JHEP06(2020)027 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Super-Schwarzians via nonlinear realizations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="2004.04489v2-abstract-short" style="display: inline;"> The N=1 and N=2 super-Schwarzian derivatives were originally introduced by physicists when computing a finite superconformal transformation of the super stress-energy tensor underlying a superconformal field theory. Mathematicians like to think of them as the cocycles describing central extensions of Lie superalgebras. In this work, a third possibility is discussed which consists in applying the m… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.04489v2-abstract-full').style.display = 'inline'; document.getElementById('2004.04489v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.04489v2-abstract-full" style="display: none;"> The N=1 and N=2 super-Schwarzian derivatives were originally introduced by physicists when computing a finite superconformal transformation of the super stress-energy tensor underlying a superconformal field theory. Mathematicians like to think of them as the cocycles describing central extensions of Lie superalgebras. In this work, a third possibility is discussed which consists in applying the method of nonlinear realizations to osp(1|2) and su(1,1|1) superconformal algebras. It is demonstrated that the super-Schwarzians arise quite naturally, if one decides to keep the number of independent Goldstone superfields to a minimum. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.04489v2-abstract-full').style.display = 'none'; document.getElementById('2004.04489v2-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> 17 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </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">V2: 14 pages; presentation improved in the introductory and concluding sections, two refs. added; the version to appear in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.13339">arXiv:1912.13339</a> <span> [<a href="https://arxiv.org/pdf/1912.13339">pdf</a>, <a href="https://arxiv.org/ps/1912.13339">ps</a>, <a href="https://arxiv.org/format/1912.13339">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="General Relativity and Quantum Cosmology">gr-qc</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/10.1007/JHEP03(2020)143">10.1007/JHEP03(2020)143 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Bianchi type-V spinning particle on 2-sphere </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1912.13339v1-abstract-short" style="display: inline;"> Integrable spinning extension of a free particle on 2-sphere is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two quadratic constants of the motion, or external field of the Dirac monopole, or the motion on the group manifold of SU(2) are built. A link to the model of a rela… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.13339v1-abstract-full').style.display = 'inline'; document.getElementById('1912.13339v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.13339v1-abstract-full" style="display: none;"> Integrable spinning extension of a free particle on 2-sphere is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two quadratic constants of the motion, or external field of the Dirac monopole, or the motion on the group manifold of SU(2) are built. A link to the model of a relativistic spinning particle propagating on the near horizon 7d Myers-Perry black hole background is considered. Implications of the construction in this work for the D(2,1;a) superconformal mechanics are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.13339v1-abstract-full').style.display = 'none'; document.getElementById('1912.13339v1-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, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </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> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.04820">arXiv:1909.04820</a> <span> [<a href="https://arxiv.org/pdf/1909.04820">pdf</a>, <a href="https://arxiv.org/ps/1909.04820">ps</a>, <a href="https://arxiv.org/format/1909.04820">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey 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/10.1103/PhysRevD.100.128501">10.1103/PhysRevD.100.128501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Comment on "Generalized near horizon extreme binary black hole geometry" </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1909.04820v2-abstract-short" style="display: inline;"> It is demonstrated that the near-horizon geometry of two extreme Kerr black holes of equal mass, which are held a finite distance apart by a massless strut, introduced recently in [Phys. Rev. D 100 (2019) 044033], is a particular member of the near horizon Kerr-Bolt class. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.04820v2-abstract-full" style="display: none;"> It is demonstrated that the near-horizon geometry of two extreme Kerr black holes of equal mass, which are held a finite distance apart by a massless strut, introduced recently in [Phys. Rev. D 100 (2019) 044033], is a particular member of the near horizon Kerr-Bolt class. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.04820v2-abstract-full').style.display = 'none'; document.getElementById('1909.04820v2-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 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </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">V2: 4 pages. A typo fixed in the abstract and text, one ref. updated. The version to appear in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 100, 128501 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.01935">arXiv:1905.01935</a> <span> [<a href="https://arxiv.org/pdf/1905.01935">pdf</a>, <a href="https://arxiv.org/ps/1905.01935">ps</a>, <a href="https://arxiv.org/format/1905.01935">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> </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.2019.05.054">10.1016/j.physletb.2019.05.054 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Schwarzian mechanics via nonlinear realizations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1905.01935v2-abstract-short" style="display: inline;"> The method of nonlinear realizations is used to clarify some conceptual and technical issues related to the Schwarzian mechanics. It is shown that the Schwarzian derivative arises naturally, if one applies the method to SL(2,R) times R group and decides to keep the number of the independent Goldstone fields to a minimum. The Schwarzian derivative is linked to the invariant Maurer-Cartan one-forms,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.01935v2-abstract-full').style.display = 'inline'; document.getElementById('1905.01935v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.01935v2-abstract-full" style="display: none;"> The method of nonlinear realizations is used to clarify some conceptual and technical issues related to the Schwarzian mechanics. It is shown that the Schwarzian derivative arises naturally, if one applies the method to SL(2,R) times R group and decides to keep the number of the independent Goldstone fields to a minimum. The Schwarzian derivative is linked to the invariant Maurer-Cartan one-forms, which make its SL(2,R)-invariance manifest. A Lagrangian formulation for a variant of the Schwarzian mechanics studied recently in [Nucl. Phys. B 936 (2018) 661] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.01935v2-abstract-full').style.display = 'none'; document.getElementById('1905.01935v2-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 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2019. </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">V2: 9 pages, minor improvements, the version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.03996">arXiv:1904.03996</a> <span> [<a href="https://arxiv.org/pdf/1904.03996">pdf</a>, <a href="https://arxiv.org/format/1904.03996">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="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/10.1007/JHEP06(2019)061">10.1007/JHEP06(2019)061 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=2 supersymmetric extensions of relativistic Toda lattice </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1904.03996v2-abstract-short" style="display: inline;"> N=2 supersymmetric extensions of both the periodic and non-periodic relativistic Toda lattice are built within the framework of the Hamiltonian formalism. A geodesic description in terms of a non-metric connection is discussed. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.03996v2-abstract-full" style="display: none;"> N=2 supersymmetric extensions of both the periodic and non-periodic relativistic Toda lattice are built within the framework of the Hamiltonian formalism. A geodesic description in terms of a non-metric connection is discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.03996v2-abstract-full').style.display = 'none'; document.getElementById('1904.03996v2-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 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </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">v2: 10 pages, concluding section extended, two refs. added, the version to appear in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08012">arXiv:1902.08012</a> <span> [<a href="https://arxiv.org/pdf/1902.08012">pdf</a>, <a href="https://arxiv.org/ps/1902.08012">ps</a>, <a href="https://arxiv.org/format/1902.08012">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> </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.2019.114618">10.1016/j.nuclphysb.2019.114618 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Casimir operators of centrally extended l-conformal Galilei algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1902.08012v1-abstract-short" style="display: inline;"> The full set of Casimir elements of the centrally extended l-conformal Galilei algebra is found in simple and tractable form. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08012v1-abstract-full" style="display: none;"> The full set of Casimir elements of the centrally extended l-conformal Galilei algebra is found in simple and tractable form. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08012v1-abstract-full').style.display = 'none'; document.getElementById('1902.08012v1-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 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </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</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.06851">arXiv:1902.06851</a> <span> [<a href="https://arxiv.org/pdf/1902.06851">pdf</a>, <a href="https://arxiv.org/format/1902.06851">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/10.1007/JHEP03(2019)069">10.1007/JHEP03(2019)069 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spinning extensions of $D(2,1;伪)$ superconformal mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Lechtenfeld%2C+O">Olaf Lechtenfeld</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="1902.06851v1-abstract-short" style="display: inline;"> As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;伪)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of $D(2,1;伪)$ superconformal mechanics by adjusting the SU(2) generators associated with… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.06851v1-abstract-full').style.display = 'inline'; document.getElementById('1902.06851v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.06851v1-abstract-full" style="display: none;"> As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;伪)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of $D(2,1;伪)$ superconformal mechanics by adjusting the SU(2) generators associated with the relativistic spinning particle coupled to a spherically symmetric Einstein-Maxwell background. The angular sector of the full superconformal system corresponds to the orbital motion of a particle coupled to a symmetric Euler top, which represents the spin degrees of freedom. This particle moves either on the two-sphere, optionally in the external field of a Dirac monopole, or in the SU(2) group manifold. Each case is proven to be superintegrable, and explicit solutions are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.06851v1-abstract-full').style.display = 'none'; document.getElementById('1902.06851v1-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 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </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">1+14 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/1901.03699">arXiv:1901.03699</a> <span> [<a href="https://arxiv.org/pdf/1901.03699">pdf</a>, <a href="https://arxiv.org/ps/1901.03699">ps</a>, <a href="https://arxiv.org/format/1901.03699">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Physics">physics.class-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/s10052-019-6812-6">10.1140/epjc/s10052-019-6812-6 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Eisenhart Lift of $2$--Dimensional Mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Fordy%2C+A+P">Allan P. Fordy</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1901.03699v1-abstract-short" style="display: inline;"> The Eisenhart lift is a variant of geometrization of classical mechanics with $d$ degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on $(d+2)$-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of $2$-dimensional mechanics on curved background is studied. The corresponding $4$-dimensional met… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1901.03699v1-abstract-full').style.display = 'inline'; document.getElementById('1901.03699v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1901.03699v1-abstract-full" style="display: none;"> The Eisenhart lift is a variant of geometrization of classical mechanics with $d$ degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on $(d+2)$-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of $2$-dimensional mechanics on curved background is studied. The corresponding $4$-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy--momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of $2$-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the $2$-dimensional Darboux--Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1901.03699v1-abstract-full').style.display = 'none'; document.getElementById('1901.03699v1-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> 10 January, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2019. </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> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 17B63; 37J35; 70G45; 70H06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1809.00904">arXiv:1809.00904</a> <span> [<a href="https://arxiv.org/pdf/1809.00904">pdf</a>, <a href="https://arxiv.org/ps/1809.00904">ps</a>, <a href="https://arxiv.org/format/1809.00904">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.nuclphysb.2018.10.004">10.1016/j.nuclphysb.2018.10.004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A variant of Schwarzian mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1809.00904v2-abstract-short" style="display: inline;"> The Schwarzian derivative is invariant under SL(2,R)-transformations and, as thus, any function of it can be used to determine the equation of motion or the Lagrangian density of a higher derivative SL(2,R)-invariant 1d mechanics or the Schwarzian mechanics for short. In this note, we consider the simplest variant which results from setting the Schwarzian derivative to be equal to a dimensionful c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.00904v2-abstract-full').style.display = 'inline'; document.getElementById('1809.00904v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1809.00904v2-abstract-full" style="display: none;"> The Schwarzian derivative is invariant under SL(2,R)-transformations and, as thus, any function of it can be used to determine the equation of motion or the Lagrangian density of a higher derivative SL(2,R)-invariant 1d mechanics or the Schwarzian mechanics for short. In this note, we consider the simplest variant which results from setting the Schwarzian derivative to be equal to a dimensionful coupling constant. It is shown that the corresponding dynamical system in general undergoes stable evolution but for one fixed point solution which is only locally stable. Conserved charges associated with the SL(2,R)-symmetry transformations are constructed and a Hamiltonian formulation reproducing them is proposed. An embedding of the Schwarzian mechanics into a larger dynamical system associated with the geodesics of a Brinkmann-like metric obeying the Einstein equations is constructed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.00904v2-abstract-full').style.display = 'none'; document.getElementById('1809.00904v2-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> 8 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2018. </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">V2: 8 pages, typos fixed. The version to appear in NPB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.08011">arXiv:1802.08011</a> <span> [<a href="https://arxiv.org/pdf/1802.08011">pdf</a>, <a href="https://arxiv.org/ps/1802.08011">ps</a>, <a href="https://arxiv.org/format/1802.08011">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/JHEP04(2018)079">10.1007/JHEP04(2018)079 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ruijsenaars-Schneider three-body models with N=2 supersymmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1802.08011v3-abstract-short" style="display: inline;"> The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also k… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.08011v3-abstract-full').style.display = 'inline'; document.getElementById('1802.08011v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.08011v3-abstract-full" style="display: none;"> The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.08011v3-abstract-full').style.display = 'none'; document.getElementById('1802.08011v3-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 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </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">v3: 10 pages, imaginary unit missed in Eq. (22) is reinstated</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.03370">arXiv:1802.03370</a> <span> [<a href="https://arxiv.org/pdf/1802.03370">pdf</a>, <a href="https://arxiv.org/format/1802.03370">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</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="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/s10052-018-5789-x">10.1140/epjc/s10052-018-5789-x <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Cosmological aspects of the Eisenhart-Duval lift </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Cariglia%2C+M">M. Cariglia</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">A. Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Gibbons%2C+G+W">G. W. Gibbons</a>, <a href="/search/hep-th?searchtype=author&query=Horvathy%2C+P+A">P. A. Horvathy</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="1802.03370v3-abstract-short" style="display: inline;"> A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton--Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cos… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.03370v3-abstract-full').style.display = 'inline'; document.getElementById('1802.03370v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.03370v3-abstract-full" style="display: none;"> A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton--Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart--Duval framework is presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.03370v3-abstract-full').style.display = 'none'; document.getElementById('1802.03370v3-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> 10 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </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">Minor corrections and precisions, a couple of references added. 34 pages, 3 figures. To be published in European Physical Journal C</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.00742">arXiv:1712.00742</a> <span> [<a href="https://arxiv.org/pdf/1712.00742">pdf</a>, <a href="https://arxiv.org/ps/1712.00742">ps</a>, <a href="https://arxiv.org/format/1712.00742">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="General Relativity and Quantum Cosmology">gr-qc</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/s10052-018-5568-8">10.1140/epjc/s10052-018-5568-8 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Geometry of the isotropic oscillator driven by the conformal mode </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1712.00742v3-abstract-short" style="display: inline;"> Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. The conventional methods include the Jacobi metric and the Eisenhart lift. In this work, a modification of the Eisenhart lift is proposed which describes the isotropic oscillator in arbitrary dimension driven by the one-dimen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.00742v3-abstract-full').style.display = 'inline'; document.getElementById('1712.00742v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.00742v3-abstract-full" style="display: none;"> Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. The conventional methods include the Jacobi metric and the Eisenhart lift. In this work, a modification of the Eisenhart lift is proposed which describes the isotropic oscillator in arbitrary dimension driven by the one-dimensional conformal mode. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.00742v3-abstract-full').style.display = 'none'; document.getElementById('1712.00742v3-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> 16 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </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">V3: 10 pages, presentation improved, the version to appear in Eur. Phys. J. C</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1706.08300">arXiv:1706.08300</a> <span> [<a href="https://arxiv.org/pdf/1706.08300">pdf</a>, <a href="https://arxiv.org/ps/1706.08300">ps</a>, <a href="https://arxiv.org/format/1706.08300">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(2017)131">10.1007/JHEP09(2017)131 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Krivonos%2C+S">Sergey Krivonos</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="1706.08300v2-abstract-short" style="display: inline;"> N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators in the superalgebra form analogues of the irreducible (1,4,3)-, (2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a turns out to be con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.08300v2-abstract-full').style.display = 'inline'; document.getElementById('1706.08300v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1706.08300v2-abstract-full" style="display: none;"> N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators in the superalgebra form analogues of the irreducible (1,4,3)-, (2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a turns out to be constrained by the Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2,1;a), a remains arbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.08300v2-abstract-full').style.display = 'none'; document.getElementById('1706.08300v2-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 September, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2017. </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">V2: 9 pages. Introductory part extended, two references added. The version to appear in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.02814">arXiv:1705.02814</a> <span> [<a href="https://arxiv.org/pdf/1705.02814">pdf</a>, <a href="https://arxiv.org/ps/1705.02814">ps</a>, <a href="https://arxiv.org/format/1705.02814">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.2017.05.086">10.1016/j.physletb.2017.05.086 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=4 l-conformal Galilei superalgebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1705.02814v3-abstract-short" style="display: inline;"> An N=4 supersymmetric extension of the l-conformal Galilei algebra is constructed. This is achieved by combining generators of spatial symmetries from the l-conformal Galilei algebra and those underlying the most general superconformal group in one dimension D(2,1;a). The value of the group parameter a is fixed from the requirement that the resulting superalgebra is finite-dimensional. The analysi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.02814v3-abstract-full').style.display = 'inline'; document.getElementById('1705.02814v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.02814v3-abstract-full" style="display: none;"> An N=4 supersymmetric extension of the l-conformal Galilei algebra is constructed. This is achieved by combining generators of spatial symmetries from the l-conformal Galilei algebra and those underlying the most general superconformal group in one dimension D(2,1;a). The value of the group parameter a is fixed from the requirement that the resulting superalgebra is finite-dimensional. The analysis reveals a=-1/2 thus reducing D(2,1;a) to OSp(4|2). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.02814v3-abstract-full').style.display = 'none'; document.getElementById('1705.02814v3-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 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </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">V3:11 pages. Two misprints in the introduction corrected. The version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1702.01955">arXiv:1702.01955</a> <span> [<a href="https://arxiv.org/pdf/1702.01955">pdf</a>, <a href="https://arxiv.org/ps/1702.01955">ps</a>, <a href="https://arxiv.org/format/1702.01955">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="General Relativity and Quantum Cosmology">gr-qc</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(2017)054">10.1007/JHEP03(2017)054 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspective </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1702.01955v2-abstract-short" style="display: inline;"> Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can be extended to a representation of the Lie superalgebra corresponding to D(2,1;a). Novel couplings of arbitrary number of supermultiplets of the typ… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.01955v2-abstract-full').style.display = 'inline'; document.getElementById('1702.01955v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1702.01955v2-abstract-full" style="display: none;"> Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can be extended to a representation of the Lie superalgebra corresponding to D(2,1;a). Novel couplings of arbitrary number of supermultiplets of the type (1,4,3) and (0,4,4) with a single supermultiplet of either the type (3,4,1), or (4,4,0) are constructed. D(2,1;a) superconformal mechanics describing superparticles propagating near the horizon of the extreme Reissner-Nordstrom-AdS-dS black hole in four and five dimensions is considered. The parameter a is linked to the cosmological constant. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.01955v2-abstract-full').style.display = 'none'; document.getElementById('1702.01955v2-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 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2017. </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">V2:15 pages. Lagrangian formulations in Sect. 3, one reference and acknowledgement added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.04294">arXiv:1611.04294</a> <span> [<a href="https://arxiv.org/pdf/1611.04294">pdf</a>, <a href="https://arxiv.org/ps/1611.04294">ps</a>, <a href="https://arxiv.org/format/1611.04294">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.2016.11.059">10.1016/j.physletb.2016.11.059 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Eisenhart lift for higher derivative systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1611.04294v2-abstract-short" style="display: inline;"> The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of poten… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.04294v2-abstract-full').style.display = 'inline'; document.getElementById('1611.04294v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.04294v2-abstract-full" style="display: none;"> The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais-Uhlenbeck oscillator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.04294v2-abstract-full').style.display = 'none'; document.getElementById('1611.04294v2-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 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </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">V2: 12 pages, minor improvements, references added; the version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1606.05230">arXiv:1606.05230</a> <span> [<a href="https://arxiv.org/pdf/1606.05230">pdf</a>, <a href="https://arxiv.org/ps/1606.05230">ps</a>, <a href="https://arxiv.org/format/1606.05230">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(2016)114">10.1007/JHEP09(2016)114 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Superconformal SU(1,1|n) mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Lechtenfeld%2C+O">Olaf Lechtenfeld</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="1606.05230v2-abstract-short" style="display: inline;"> Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1,1|2) in mechanics. Remarking that SU(1,1|2) is a particular member of a chain of supergroups SU(1,1|n) parametrized by an integer n, here we begin a systematic study of SU(1,1|n) multi-particle mechanics. A representation of the superconformal algebra su(1,1|n) is constructed on the phase space… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.05230v2-abstract-full').style.display = 'inline'; document.getElementById('1606.05230v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1606.05230v2-abstract-full" style="display: none;"> Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1,1|2) in mechanics. Remarking that SU(1,1|2) is a particular member of a chain of supergroups SU(1,1|n) parametrized by an integer n, here we begin a systematic study of SU(1,1|n) multi-particle mechanics. A representation of the superconformal algebra su(1,1|n) is constructed on the phase space spanned by m copies of the (1,2n,2n-1) supermultiplet. We show that the dynamics is governed by two prepotentials V and F, and the Witten-Dijkgraaf-Verlinde-Verlinde equation for F shows up as a consequence of a more general fourth-order equation. All solutions to the latter in terms of root systems reveal decoupled models only. An extension of the dynamical content of the (1,2n,2n-1) supermultiplet by angular variables in a way similar to the SU(1,1|2) case is problematic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.05230v2-abstract-full').style.display = 'none'; document.getElementById('1606.05230v2-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> 8 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2016. </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">1+8 pages; v2: eq.(14) corrected, one ref. added, published version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1604.08056">arXiv:1604.08056</a> <span> [<a href="https://arxiv.org/pdf/1604.08056">pdf</a>, <a href="https://arxiv.org/ps/1604.08056">ps</a>, <a href="https://arxiv.org/format/1604.08056">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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="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/s10052-016-4333-0">10.1140/epjc/s10052-016-4333-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the near horizon rotating black hole geometries with NUT charges </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Orekhov%2C+K">Kirill Orekhov</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="1604.08056v1-abstract-short" style="display: inline;"> The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d=4 and d=5 where the vacuum Einstein equations reduce to a coupled s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.08056v1-abstract-full').style.display = 'inline'; document.getElementById('1604.08056v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1604.08056v1-abstract-full" style="display: none;"> The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d=4 and d=5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d=4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d=5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d=5 near horizon Myers-Perry black hole with a NUT charge. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.08056v1-abstract-full').style.display = 'none'; document.getElementById('1604.08056v1-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 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2016. </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> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1512.06226">arXiv:1512.06226</a> <span> [<a href="https://arxiv.org/pdf/1512.06226">pdf</a>, <a href="https://arxiv.org/ps/1512.06226">ps</a>, <a href="https://arxiv.org/format/1512.06226">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="General Relativity and Quantum Cosmology">gr-qc</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.2016.01.042">10.1016/j.physletb.2016.01.042 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ricci-flat spacetimes with l-conformal Galilei symmetry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Chernyavsky%2C+D">D. Chernyavsky</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">A. Galajinsky</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="1512.06226v2-abstract-short" style="display: inline;"> Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations are shown to describe a second order dynamical system for which the acceleration generators are functionally independent. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1512.06226v2-abstract-full" style="display: none;"> Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations are shown to describe a second order dynamical system for which the acceleration generators are functionally independent. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1512.06226v2-abstract-full').style.display = 'none'; document.getElementById('1512.06226v2-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 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 December, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2015. </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">V2: refs. added, the version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1504.03826">arXiv:1504.03826</a> <span> [<a href="https://arxiv.org/pdf/1504.03826">pdf</a>, <a href="https://arxiv.org/ps/1504.03826">ps</a>, <a href="https://arxiv.org/format/1504.03826">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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="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/10.1103/PhysRevD.91.104020">10.1103/PhysRevD.91.104020 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Self-dual metrics with maximally superintegrable geodesic flows </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Filyukov%2C+S">Sergei Filyukov</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1504.03826v2-abstract-short" style="display: inline;"> A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-Euclidean spacetime of signature (1,1). It is characterized by the presence of a second rank Killing tensor. Spacetimes of the ultrahyperbolic signature (2,q) with q > 2, which admit a second rank Killing tensor and possess sup… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.03826v2-abstract-full').style.display = 'inline'; document.getElementById('1504.03826v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1504.03826v2-abstract-full" style="display: none;"> A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-Euclidean spacetime of signature (1,1). It is characterized by the presence of a second rank Killing tensor. Spacetimes of the ultrahyperbolic signature (2,q) with q > 2, which admit a second rank Killing tensor and possess superintegrable geodesic flows, are built. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.03826v2-abstract-full').style.display = 'none'; document.getElementById('1504.03826v2-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 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2015. </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">V2: 11 pages, minor modifications</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 91, 104020 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.08633">arXiv:1503.08633</a> <span> [<a href="https://arxiv.org/pdf/1503.08633">pdf</a>, <a href="https://arxiv.org/ps/1503.08633">ps</a>, <a href="https://arxiv.org/format/1503.08633">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.2015.04.024">10.1016/j.nuclphysb.2015.04.024 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1503.08633v2-abstract-short" style="display: inline;"> In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013) 405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015) 031701], representation theory of the centrally extended l-conformal Galilei algebra with half-integer l has been applied so as to construct second order differential equations exhibiting the corresponding group as kinematical symmetry. It was sugges… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.08633v2-abstract-full').style.display = 'inline'; document.getElementById('1503.08633v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.08633v2-abstract-full" style="display: none;"> In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013) 405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015) 031701], representation theory of the centrally extended l-conformal Galilei algebra with half-integer l has been applied so as to construct second order differential equations exhibiting the corresponding group as kinematical symmetry. It was suggested to treat them as the Schrodinger equations which involve Hamiltonians describing dynamical systems without higher derivatives. The Hamiltonians possess two unusual features, however. First, they involve the standard kinetic term only for one degree of freedom, while the remaining variables provide contributions linear in momenta. This is typical for Ostrogradsky's canonical approach to the description of higher derivative systems. Second, the Hamiltonian in the second paper is not Hermitian in the conventional sense. In this work, we study the classical limit of the quantum Hamiltonians and demonstrate that the first of them is equivalent to the Hamiltonian describing free higher derivative nonrelativistic particles, while the second can be linked to the Pais-Uhlenbeck oscillator whose frequencies form the arithmetic sequence omega_k=(2k-1), k=1,...,n. We also confront the higher derivative models with a genuine second order system constructed in our recent work [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212] which is discussed in detail for l=3/2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.08633v2-abstract-full').style.display = 'none'; document.getElementById('1503.08633v2-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> 29 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 March, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2015. </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">V2:12 pages,clarifying remarks included into the Introduction and Conclusion, the version to appear in NPB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.02162">arXiv:1503.02162</a> <span> [<a href="https://arxiv.org/pdf/1503.02162">pdf</a>, <a href="https://arxiv.org/ps/1503.02162">ps</a>, <a href="https://arxiv.org/format/1503.02162">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</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="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.2015.04.001">10.1016/j.physletb.2015.04.001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ricci-flat spacetimes admitting higher rank Killing tensors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Cariglia%2C+M">Marco Cariglia</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1503.02162v1-abstract-short" style="display: inline;"> Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.02162v1-abstract-full" style="display: none;"> Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.02162v1-abstract-full').style.display = 'none'; document.getElementById('1503.02162v1-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 March, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2015. </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> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.4467">arXiv:1412.4467</a> <span> [<a href="https://arxiv.org/pdf/1412.4467">pdf</a>, <a href="https://arxiv.org/ps/1412.4467">ps</a>, <a href="https://arxiv.org/format/1412.4467">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/10.1007/JHEP02(2015)091">10.1007/JHEP02(2015)091 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=4 superconformal mechanics from the su(2) perspective </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1412.4467v2-abstract-short" style="display: inline;"> The issue of constructing an N=4 superconformal mechanics in one dimension is reconsidered with a special emphasis put on the realizations of the su(2)-subalgebra in the full su(1,1|2)-superalgebra. New dynamical realizations of su(1,1|2) are constructed which describe an interaction of the (0,4,4)-supermultiplet with either the (1,4,3)-, or (3,4,1)-, or (4,4,0)-supermultiplet. A relation of the N… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.4467v2-abstract-full').style.display = 'inline'; document.getElementById('1412.4467v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.4467v2-abstract-full" style="display: none;"> The issue of constructing an N=4 superconformal mechanics in one dimension is reconsidered with a special emphasis put on the realizations of the su(2)-subalgebra in the full su(1,1|2)-superalgebra. New dynamical realizations of su(1,1|2) are constructed which describe an interaction of the (0,4,4)-supermultiplet with either the (1,4,3)-, or (3,4,1)-, or (4,4,0)-supermultiplet. A relation of the N=4 superconformal mechanics with massive superparticles propagating near the black hole horizons is discussed. Background geometry associated with the model based on the (4,4,0)-supermultiplet is identified with the near horizon limit of the d=5, N=2 supergravity interacting with one vector multiplet. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.4467v2-abstract-full').style.display = 'none'; document.getElementById('1412.4467v2-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, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </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">V2: 16 pages, minor modifications, references added, acknowledgements extended; the version to appear in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.1297">arXiv:1402.1297</a> <span> [<a href="https://arxiv.org/pdf/1402.1297">pdf</a>, <a href="https://arxiv.org/ps/1402.1297">ps</a>, <a href="https://arxiv.org/format/1402.1297">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.2014.05.025">10.1016/j.nuclphysb.2014.05.025 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Andrzejewski%2C+K">Krzysztof Andrzejewski</a>, <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Gonera%2C+J">Joanna Gonera</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1402.1297v3-abstract-short" style="display: inline;"> It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence omega_k=(2k-1) omega_1, where k=1,...,n, and l is the half-integer (2n-1)/2. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.1297v3-abstract-full').style.display = 'inline'; document.getElementById('1402.1297v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.1297v3-abstract-full" style="display: none;"> It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence omega_k=(2k-1) omega_1, where k=1,...,n, and l is the half-integer (2n-1)/2. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton-Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.1297v3-abstract-full').style.display = 'none'; document.getElementById('1402.1297v3-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 June, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </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">V3:Introduction extended, one reference added. The version to appear in NPB</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-1/14 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1306.5238">arXiv:1306.5238</a> <span> [<a href="https://arxiv.org/pdf/1306.5238">pdf</a>, <a href="https://arxiv.org/ps/1306.5238">ps</a>, <a href="https://arxiv.org/format/1306.5238">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="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/10.1007/JHEP09(2013)113">10.1007/JHEP09(2013)113 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On two-dimensional integrable models with a cubic or quartic integral of motion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Lechtenfeld%2C+O">Olaf Lechtenfeld</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="1306.5238v2-abstract-short" style="display: inline;"> Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance under continuous rescalings and a dihedral symmetry, we construct new integrable models with a cubic or quartic integral, each of which involves either one or tw… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1306.5238v2-abstract-full').style.display = 'inline'; document.getElementById('1306.5238v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1306.5238v2-abstract-full" style="display: none;"> Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance under continuous rescalings and a dihedral symmetry, we construct new integrable models with a cubic or quartic integral, each of which involves either one or two continuous parameters. A reducible case related to the two-dimensional wave equation is discussed as well. We conjecture a hidden D_{2n} dihedral symmetry for models with an integral of n-th order in the velocities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1306.5238v2-abstract-full').style.display = 'none'; document.getElementById('1306.5238v2-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 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2013. </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">1+10 pages; v2: structure improved, introduction extended, one ref. added, version published in JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.4901">arXiv:1303.4901</a> <span> [<a href="https://arxiv.org/pdf/1303.4901">pdf</a>, <a href="https://arxiv.org/ps/1303.4901">ps</a>, <a href="https://arxiv.org/format/1303.4901">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="General Relativity and Quantum Cosmology">gr-qc</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/10.1007/JHEP06(2013)002">10.1007/JHEP06(2013)002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Nersessian%2C+A">Armen Nersessian</a>, <a href="/search/hep-th?searchtype=author&query=Saghatelian%2C+A">Armen Saghatelian</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="1303.4901v1-abstract-short" style="display: inline;"> We provide a systematic account of integrability of the spherical mechanics associated with the near horizon extremal Myers-Perry black hole in arbitrary dimension for the special case that all rotation parameters are equal. The integrability is established both in the original coordinates and in action-angle variables. It is demonstrated that the spherical mechanics associated with the black hole… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.4901v1-abstract-full').style.display = 'inline'; document.getElementById('1303.4901v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.4901v1-abstract-full" style="display: none;"> We provide a systematic account of integrability of the spherical mechanics associated with the near horizon extremal Myers-Perry black hole in arbitrary dimension for the special case that all rotation parameters are equal. The integrability is established both in the original coordinates and in action-angle variables. It is demonstrated that the spherical mechanics associated with the black hole in d=2n+1 is maximally superintegrable, while its counterpart related to the black hole in d=2n lacks for only one integral of motion to be maximally superintegrable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.4901v1-abstract-full').style.display = 'none'; document.getElementById('1303.4901v1-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 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </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">Journal ref:</span> JHEP 1306 (2013) 002 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.3419">arXiv:1303.3419</a> <span> [<a href="https://arxiv.org/pdf/1303.3419">pdf</a>, <a href="https://arxiv.org/ps/1303.3419">ps</a>, <a href="https://arxiv.org/format/1303.3419">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.2013.04.054">10.1016/j.physletb.2013.04.054 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamical realizations of l-conformal Newton-Hooke group </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1303.3419v1-abstract-short" style="display: inline;"> The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effec… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.3419v1-abstract-full').style.display = 'inline'; document.getElementById('1303.3419v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.3419v1-abstract-full" style="display: none;"> The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effective external field.The dynamical system describes a generalized multi-dimensional oscillator, which undergoes accelerated/decelerated motion in an ellipse in accord with evolution of the conformal mode. Higher derivative formulations are discussed as well. It is demonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the l=3/2-conformal Newton-Hooke symmetry for a particular choice of its frequencies. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.3419v1-abstract-full').style.display = 'none'; document.getElementById('1303.3419v1-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 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </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> LMP-TPU-05/13 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.1159">arXiv:1301.1159</a> <span> [<a href="https://arxiv.org/pdf/1301.1159">pdf</a>, <a href="https://arxiv.org/ps/1301.1159">ps</a>, <a href="https://arxiv.org/format/1301.1159">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey 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/10.1103/PhysRevD.88.027505">10.1103/PhysRevD.88.027505 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Near horizon geometry of extremal black holes and Banados-Silk-West effect </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1301.1159v5-abstract-short" style="display: inline;"> Recently, Banados, Silk and West analyzed a collision of two particles near the horizon of the extremal Kerr black hole and demonstrated that the energy in the center-of-mass frame can be arbitrarily large provided the angular momentum of one of the colliding particles takes a special value. As is known, the vicinity of the extremal Kerr black hole horizon can be viewed as a complete vacuum spacet… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.1159v5-abstract-full').style.display = 'inline'; document.getElementById('1301.1159v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.1159v5-abstract-full" style="display: none;"> Recently, Banados, Silk and West analyzed a collision of two particles near the horizon of the extremal Kerr black hole and demonstrated that the energy in the center-of-mass frame can be arbitrarily large provided the angular momentum of one of the colliding particles takes a special value. As is known, the vicinity of the extremal Kerr black hole horizon can be viewed as a complete vacuum spacetime in its own right. In this work, we consider a collision of two neutral particles within the context of the near horizon extremal Kerr geometry and demonstrate that the energy in the center-of-mass frame is finite for any admissible value of the particle parameters. An explanation of why the two approaches disagree on the Banados-Silk-West effect is given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.1159v5-abstract-full').style.display = 'none'; document.getElementById('1301.1159v5-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 July, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </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">V5:10 pages, major revision, title changed; the version published in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-01/13 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D88 (2013) 027505 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1209.5034">arXiv:1209.5034</a> <span> [<a href="https://arxiv.org/pdf/1209.5034">pdf</a>, <a href="https://arxiv.org/ps/1209.5034">ps</a>, <a href="https://arxiv.org/format/1209.5034">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="General Relativity and Quantum Cosmology">gr-qc</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.87.024023">10.1103/PhysRevD.87.024023 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Near horizon black holes in diverse dimensions and integrable models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1209.5034v2-abstract-short" style="display: inline;"> The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally symmetric configuration and derive from it a new integrable Hamiltonian mechanics with U(n) symmetry. A further reduction of the model is discussed, which is o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.5034v2-abstract-full').style.display = 'inline'; document.getElementById('1209.5034v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1209.5034v2-abstract-full" style="display: none;"> The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally symmetric configuration and derive from it a new integrable Hamiltonian mechanics with U(n) symmetry. A further reduction of the model is discussed, which is obtained by discarding cyclic variables. A variant of the Higgs oscillator and the Poschl-Teller system show up in four and five dimensions, respectively. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.5034v2-abstract-full').style.display = 'none'; document.getElementById('1209.5034v2-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 December, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 September, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2012. </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">V2: 17 pages, minor modifications</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-11/12 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1208.1403">arXiv:1208.1403</a> <span> [<a href="https://arxiv.org/pdf/1208.1403">pdf</a>, <a href="https://arxiv.org/ps/1208.1403">ps</a>, <a href="https://arxiv.org/format/1208.1403">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.2012.09.004">10.1016/j.nuclphysb.2012.09.004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamical realization of l-conformal Galilei algebra and oscillators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1208.1403v2-abstract-short" style="display: inline;"> The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which parametrize particles in d spatial dimensions, and a conformal mode, which gives rise to an effective external field. It is shown that trajectories of the system… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.1403v2-abstract-full').style.display = 'inline'; document.getElementById('1208.1403v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1208.1403v2-abstract-full" style="display: none;"> The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which parametrize particles in d spatial dimensions, and a conformal mode, which gives rise to an effective external field. It is shown that trajectories of the system can be mapped into those of a set of decoupled oscillators in d dimensions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.1403v2-abstract-full').style.display = 'none'; document.getElementById('1208.1403v2-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 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2012. </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">V2: minor text improvements</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-9/12 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1201.3085">arXiv:1201.3085</a> <span> [<a href="https://arxiv.org/pdf/1201.3085">pdf</a>, <a href="https://arxiv.org/ps/1201.3085">ps</a>, <a href="https://arxiv.org/format/1201.3085">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="General Relativity and Quantum Cosmology">gr-qc</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.85.085002">10.1103/PhysRevD.85.085002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higher rank Killing tensors and Calogero model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</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="1201.3085v2-abstract-short" style="display: inline;"> (n+2)-dimensional Lorentzian spacetime which admits irreducible Killing tensors of rank up to n is constructed by applying the Eisenhart lift to the Calogero model. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1201.3085v2-abstract-full" style="display: none;"> (n+2)-dimensional Lorentzian spacetime which admits irreducible Killing tensors of rank up to n is constructed by applying the Eisenhart lift to the Calogero model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.3085v2-abstract-full').style.display = 'none'; document.getElementById('1201.3085v2-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, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2012. </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">V2: 12 pages, discussion extended, presentation improved, references added. The version to appear in PRD</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1108.3394">arXiv:1108.3394</a> <span> [<a href="https://arxiv.org/pdf/1108.3394">pdf</a>, <a href="https://arxiv.org/ps/1108.3394">ps</a>, <a href="https://arxiv.org/format/1108.3394">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="General Relativity and Quantum Cosmology">gr-qc</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(2011)135">10.1007/JHEP11(2011)135 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Conformal mechanics inspired by extremal black holes in d=4 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Nersessian%2C+A">Armen Nersessian</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="1108.3394v2-abstract-short" style="display: inline;"> A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1108.3394v2-abstract-full" style="display: none;"> A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1108.3394v2-abstract-full').style.display = 'none'; document.getElementById('1108.3394v2-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 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 August, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2011. </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">V2: presentation improved, new material and references added; the version to appear in JHEP</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-9/11 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 1111 (2011) 135 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1104.5115">arXiv:1104.5115</a> <span> [<a href="https://arxiv.org/pdf/1104.5115">pdf</a>, <a href="https://arxiv.org/ps/1104.5115">ps</a>, <a href="https://arxiv.org/format/1104.5115">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.2011.06.093">10.1016/j.physletb.2011.06.093 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Remarks on l-conformal extension of the Newton-Hooke algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Masterov%2C+I">Ivan Masterov</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="1104.5115v3-abstract-short" style="display: inline;"> The l-conformal extension of the Newton-Hooke algebra proposed in [J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro-Kac-Moody type extension is given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1104.5115v3-abstract-full" style="display: none;"> The l-conformal extension of the Newton-Hooke algebra proposed in [J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro-Kac-Moody type extension is given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1104.5115v3-abstract-full').style.display = 'none'; document.getElementById('1104.5115v3-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> 29 June, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 April, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2011. </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">V3: terminology improved, one reference added; the version to appear in PLB</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-7/11 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B702:265-267,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1103.1047">arXiv:1103.1047</a> <span> [<a href="https://arxiv.org/pdf/1103.1047">pdf</a>, <a href="https://arxiv.org/ps/1103.1047">ps</a>, <a href="https://arxiv.org/format/1103.1047">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.2011.04.015">10.1016/j.nuclphysb.2011.04.015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> N=2 superparticle near horizon of extreme Kerr-Newman-AdS-dS black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-th?searchtype=author&query=Galajinsky%2C+A">Anton Galajinsky</a>, <a href="/search/hep-th?searchtype=author&query=Orekhov%2C+K">Kirill Orekhov</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="1103.1047v2-abstract-short" style="display: inline;"> Conformal mechanics related to the near horizon extreme Kerr-Newman-AdS-dS black hole is studied. A unique N=2 supersymmetric extension of the conformal mechanics is constructed. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1103.1047v2-abstract-full" style="display: none;"> Conformal mechanics related to the near horizon extreme Kerr-Newman-AdS-dS black hole is studied. A unique N=2 supersymmetric extension of the conformal mechanics is constructed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.1047v2-abstract-full').style.display = 'none'; document.getElementById('1103.1047v2-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 May, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 March, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2011. </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">V2: the version to appear in NPB</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LMP-TPU-3/11 </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=Galajinsky%2C+A&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Galajinsky%2C+A&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Galajinsky%2C+A&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a 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