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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <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/2411.16176">arXiv:2411.16176</a> <span> [<a href="https://arxiv.org/pdf/2411.16176">pdf</a>, <a href="https://arxiv.org/format/2411.16176">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Yangian Form-alism for Planar Gauge Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=K%C3%B6nig%2C+B">Benedikt K枚nig</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="2411.16176v1-abstract-short" style="display: inline;"> In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology of variational forms towards a thorough derivation of the invariance statement for the undeformed action from covariance of the equations of motion under the Ya… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.16176v1-abstract-full').style.display = 'inline'; document.getElementById('2411.16176v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.16176v1-abstract-full" style="display: none;"> In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology of variational forms towards a thorough derivation of the invariance statement for the undeformed action from covariance of the equations of motion under the Yangian algebra. We then apply a twist deformation to these statements paying particular attention to cyclicity aspects. We find that the equations of motion remain covariant while invariance of the action only holds for the Yangian subalgebra that is uncharged under the twist. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.16176v1-abstract-full').style.display = 'none'; document.getElementById('2411.16176v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 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/2409.05228">arXiv:2409.05228</a> <span> [<a href="https://arxiv.org/pdf/2409.05228">pdf</a>, <a href="https://arxiv.org/format/2409.05228">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> <p class="title is-5 mathjax"> Infinite-Length Limit of Spectral Curves and Inverse Scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Gupta%2C+K">Kunal Gupta</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="2409.05228v1-abstract-short" style="display: inline;"> Integrability equips models of theoretical physics with efficient methods for the exact construction of useful states and their evolution. Relevant tools for classical integrable field models in one spatial dimensional are spectral curves in the case of periodic fields and inverse scattering for asymptotic boundary conditions. Even though the two methods are quite different in many ways, they ough… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.05228v1-abstract-full').style.display = 'inline'; document.getElementById('2409.05228v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.05228v1-abstract-full" style="display: none;"> Integrability equips models of theoretical physics with efficient methods for the exact construction of useful states and their evolution. Relevant tools for classical integrable field models in one spatial dimensional are spectral curves in the case of periodic fields and inverse scattering for asymptotic boundary conditions. Even though the two methods are quite different in many ways, they ought to be related by taking the periodicity length of closed boundary conditions to infinity. Using the Korteweg-de Vries equation and the continuous Heisenberg magnet as prototypical classical integrable field models, we discuss and illustrate how data for spectral curves transforms into asymptotic scattering data. In order to gain intuition and also for concreteness, we review how the elliptic states of these models degenerate into solitons at infinite length. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.05228v1-abstract-full').style.display = 'none'; document.getElementById('2409.05228v1-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, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">63 pages, figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UUITP-26/24 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.10327">arXiv:2401.10327</a> <span> [<a href="https://arxiv.org/pdf/2401.10327">pdf</a>, <a href="https://arxiv.org/format/2401.10327">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Affine Classical Lie Bialgebras for AdS/CFT Integrability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Im%2C+E">Egor Im</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.10327v1-abstract-short" style="display: inline;"> In this article we continue the classical analysis of the symmetry algebra underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra gl(2|2) by contraction and reduction studied in the earlier work to the case of the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine derivation natural… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.10327v1-abstract-full').style.display = 'inline'; document.getElementById('2401.10327v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.10327v1-abstract-full" style="display: none;"> In this article we continue the classical analysis of the symmetry algebra underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra gl(2|2) by contraction and reduction studied in the earlier work to the case of the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine derivation naturally measures the deviation of the classical r-matrix from the difference form. Moreover, it implements a Lorentz boost symmetry, originally suggested to be related to a q-deformed 2D Poincare algebra. We also discuss the classical double construction for the bialgebra of interest and comment on the representation of the affine structure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.10327v1-abstract-full').style.display = 'none'; document.getElementById('2401.10327v1-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 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 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/2210.11150">arXiv:2210.11150</a> <span> [<a href="https://arxiv.org/pdf/2210.11150">pdf</a>, <a href="https://arxiv.org/format/2210.11150">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.21468/SciPostPhys.14.6.157">10.21468/SciPostPhys.14.6.157 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Im%2C+E">Egor Im</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="2210.11150v2-abstract-short" style="display: inline;"> Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit of these algebraic integrable structures based on established results for the exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) whic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.11150v2-abstract-full').style.display = 'inline'; document.getElementById('2210.11150v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.11150v2-abstract-full" style="display: none;"> Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit of these algebraic integrable structures based on established results for the exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) which form supersymmetric isometries on 3D AdS space. The two major steps in this construction consist in the contraction to a 3D Poincar茅 superalgebra and a certain reduction to a deformation of the u(2|2) superalgebra. We apply these steps to the integrable structure and obtain the desired Lie bialgebras with suitable classical r-matrices of rational and trigonometric kind. We illustrate our findings in terms of representations for on-shell fields on AdS and flat space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.11150v2-abstract-full').style.display = 'none'; document.getElementById('2210.11150v2-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, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 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">44 pages, v2: minor corrections, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SciPost Phys. 14, 157 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.09110">arXiv:1804.09110</a> <span> [<a href="https://arxiv.org/pdf/1804.09110">pdf</a>, <a href="https://arxiv.org/format/1804.09110">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.21468/SciPostPhys.5.2.018">10.21468/SciPostPhys.5.2.018 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Yangian Algebra and Correlation Functions in Planar Gauge Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Garus%2C+A">Aleksander Garus</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="1804.09110v2-abstract-short" style="display: inline;"> In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as N=4 supersymmetric Yang-Mills theory with the aim to establish Ward-Takahashi identities corresponding to Yangian symmetries. To this end, we discuss the Yangian algebra relations and discover a novel set of bi-local gauge symmetries for planar gauge theories. We fix the gauge, i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.09110v2-abstract-full').style.display = 'inline'; document.getElementById('1804.09110v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.09110v2-abstract-full" style="display: none;"> In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as N=4 supersymmetric Yang-Mills theory with the aim to establish Ward-Takahashi identities corresponding to Yangian symmetries. To this end, we discuss the Yangian algebra relations and discover a novel set of bi-local gauge symmetries for planar gauge theories. We fix the gauge, introduce local and bi-local BRST symmetries and propose Slavnov-Taylor identities corresponding to the various bi-local symmetries. We then verify the validity of these identities for several correlation functions at tree and loop level. Finally, we comment on the possibility of quantum anomalies for Yangian symmetry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.09110v2-abstract-full').style.display = 'none'; document.getElementById('1804.09110v2-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 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">56 pages, v2: minor changes to address issues raised at https://scipost.org/submission/1804.09110v1/</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SciPost Phys. 5, 018 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1803.06310">arXiv:1803.06310</a> <span> [<a href="https://arxiv.org/pdf/1803.06310">pdf</a>, <a href="https://arxiv.org/format/1803.06310">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.98.046006">10.1103/PhysRevD.98.046006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Garus%2C+A">Aleksander Garus</a>, <a href="/search/math-ph?searchtype=author&query=Rosso%2C+M">Matteo Rosso</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="1803.06310v2-abstract-short" style="display: inline;"> In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how the bi-local generators act on the action of the model such that the latter becomes exactly invariant. In particular, we elaborate on the relevance of the planar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.06310v2-abstract-full').style.display = 'inline'; document.getElementById('1803.06310v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1803.06310v2-abstract-full" style="display: none;"> In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how the bi-local generators act on the action of the model such that the latter becomes exactly invariant. In particular, we elaborate on the relevance of the planar limit and how to act non-linearly with bi-local generators on the cyclic action. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.06310v2-abstract-full').style.display = 'none'; document.getElementById('1803.06310v2-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 August, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 March, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">42 pages, in honor of Joe Polchinski; v2: minor corrections</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> HU-EP-18/08 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 98, 046006 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1704.05093">arXiv:1704.05093</a> <span> [<a href="https://arxiv.org/pdf/1704.05093">pdf</a>, <a href="https://arxiv.org/format/1704.05093">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="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1751-8121/aa7a2f">10.1088/1751-8121/aa7a2f <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar茅 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Hecht%2C+R">Reimar Hecht</a>, <a href="/search/math-ph?searchtype=author&query=Hoare%2C+B">Ben Hoare</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="1704.05093v2-abstract-short" style="display: inline;"> We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the corresponding q-deformed Hopf algebra and its universal R-matrix by means of contraction. We make the curious observation that the above algebra is related to kappa-Poincar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1704.05093v2-abstract-full').style.display = 'inline'; document.getElementById('1704.05093v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1704.05093v2-abstract-full" style="display: none;"> We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the corresponding q-deformed Hopf algebra and its universal R-matrix by means of contraction. We make the curious observation that the above algebra is related to kappa-Poincar茅 symmetry. When dropping the graded part psl(2|2) we find a novel one-parameter deformation of the 3D kappa-Poincar茅 algebra. Our construction also provides a concise exact expression for its universal R-matrix. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1704.05093v2-abstract-full').style.display = 'none'; document.getElementById('1704.05093v2-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 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 April, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">25 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A. 50, 314003 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1701.09162">arXiv:1701.09162</a> <span> [<a href="https://arxiv.org/pdf/1701.09162">pdf</a>, <a href="https://arxiv.org/format/1701.09162">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.118.141603">10.1103/PhysRevLett.118.141603 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Garus%2C+A">Aleksander Garus</a>, <a href="/search/math-ph?searchtype=author&query=Rosso%2C+M">Matteo Rosso</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="1701.09162v2-abstract-short" style="display: inline;"> In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell extension of our statement which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1701.09162v2-abstract-full').style.display = 'inline'; document.getElementById('1701.09162v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1701.09162v2-abstract-full" style="display: none;"> In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell extension of our statement which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to integrable ABJM theory but not to non-integrable N=1 super-Yang-Mills theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1701.09162v2-abstract-full').style.display = 'none'; document.getElementById('1701.09162v2-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 April, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 January, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">9 pages, v2: minor changes, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> HU-EP-17/03 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 118, 141603 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1602.04988">arXiv:1602.04988</a> <span> [<a href="https://arxiv.org/pdf/1602.04988">pdf</a>, <a href="https://arxiv.org/format/1602.04988">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="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1751-8113/49/43/434005">10.1088/1751-8113/49/43/434005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Maximally extended sl(2|2) as a quantum double </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=de+Leeuw%2C+M">Marius de Leeuw</a>, <a href="/search/math-ph?searchtype=author&query=Hecht%2C+R">Reimar Hecht</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="1602.04988v1-abstract-short" style="display: inline;"> We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2) automorphism. For this maximally extended algebra we construct a consistent Hopf algebra structure where the extensions exhibit several uncommon features. We det… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.04988v1-abstract-full').style.display = 'inline'; document.getElementById('1602.04988v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1602.04988v1-abstract-full" style="display: none;"> We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2) automorphism. For this maximally extended algebra we construct a consistent Hopf algebra structure where the extensions exhibit several uncommon features. We determine the corresponding universal R-matrix containing some non-standard functions. Curiously, this Hopf algebra has one extra deformation parameter for which the R-matrix does not factorize into products of exponentials. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.04988v1-abstract-full').style.display = 'none'; document.getElementById('1602.04988v1-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 February, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">49+蔚 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A. 49, 434005 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.04838">arXiv:1503.04838</a> <span> [<a href="https://arxiv.org/pdf/1503.04838">pdf</a>, <a href="https://arxiv.org/format/1503.04838">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/10.1088/1751-8113/48/32/324002">10.1088/1751-8113/48/32/324002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fusion for the one-dimensional Hubbard model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=de+Leeuw%2C+M">Marius de Leeuw</a>, <a href="/search/math-ph?searchtype=author&query=Nag%2C+P">Panchali Nag</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="1503.04838v1-abstract-short" style="display: inline;"> We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for the one-dimensional Hubbard model. We also discuss some peculiar cases that arise in these models. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.04838v1-abstract-full" style="display: none;"> We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for the one-dimensional Hubbard model. We also discuss some peculiar cases that arise in these models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.04838v1-abstract-full').style.display = 'none'; document.getElementById('1503.04838v1-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 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">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A. 48, 324002 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1401.7691">arXiv:1401.7691</a> <span> [<a href="https://arxiv.org/pdf/1401.7691">pdf</a>, <a href="https://arxiv.org/format/1401.7691">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/10.1088/1751-8113/47/30/305201">10.1088/1751-8113/47/30/305201 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The RTT-Realization for the Deformed gl(2|2) Yangian </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=de+Leeuw%2C+M">Marius de Leeuw</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="1401.7691v2-abstract-short" style="display: inline;"> In this paper we work out the RTT-realization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying sl(2|2) Lie algebra. In our RTT-realizati… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1401.7691v2-abstract-full').style.display = 'inline'; document.getElementById('1401.7691v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1401.7691v2-abstract-full" style="display: none;"> In this paper we work out the RTT-realization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying sl(2|2) Lie algebra. In our RTT-realization we have also been able to incorporate the so-called secret symmetry and we were able to extend it to higher Yangian levels. Finally, we discuss the center of the Yangian and the automorphisms related to crossing symmetry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1401.7691v2-abstract-full').style.display = 'none'; document.getElementById('1401.7691v2-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, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 January, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">42 pages, v2: minor corrections and improvements</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A47, 305201 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1308.1584">arXiv:1308.1584</a> <span> [<a href="https://arxiv.org/pdf/1308.1584">pdf</a>, <a href="https://arxiv.org/format/1308.1584">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="Statistical Mechanics">cond-mat.stat-mech</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/10.1088/1742-5468/2013/09/P09028">10.1088/1742-5468/2013/09/P09028 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Integrable Deformations of the XXZ Spin Chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Fievet%2C+L">Lucas Fievet</a>, <a href="/search/math-ph?searchtype=author&query=de+Leeuw%2C+M">Marius de Leeuw</a>, <a href="/search/math-ph?searchtype=author&query=Loebbert%2C+F">Florian Loebbert</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="1308.1584v2-abstract-short" style="display: inline;"> We consider integrable deformations of the XXZ spin chain for periodic and open boundary conditions. In particular, we classify all long-range deformations and study their impact on the spectrum. As compared to the XXX case, we have the z-spin at our disposal, which induces two additional deformations: the short-range magnetic twist and a new long-range momentum-dependent twist. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1308.1584v2-abstract-full" style="display: none;"> We consider integrable deformations of the XXZ spin chain for periodic and open boundary conditions. In particular, we classify all long-range deformations and study their impact on the spectrum. As compared to the XXX case, we have the z-spin at our disposal, which induces two additional deformations: the short-range magnetic twist and a new long-range momentum-dependent twist. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.1584v2-abstract-full').style.display = 'none'; document.getElementById('1308.1584v2-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 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">24 pages, v2: minor changes</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Stat.Mech.1309:P09028,2013 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1207.3325">arXiv:1207.3325</a> <span> [<a href="https://arxiv.org/pdf/1207.3325">pdf</a>, <a href="https://arxiv.org/format/1207.3325">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/10.1063/1.4769824">10.1063/1.4769824 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Construction of Lax Connections by Exponentiation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Luecker%2C+F">Florian Luecker</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="1207.3325v1-abstract-short" style="display: inline;"> We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must satisfy for an entire one-parameter family of connections to be flat. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1207.3325v1-abstract-full" style="display: none;"> We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must satisfy for an entire one-parameter family of connections to be flat. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.3325v1-abstract-full').style.display = 'none'; document.getElementById('1207.3325v1-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> 13 July, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Math. Phys. 53, 122304 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.5700">arXiv:1102.5700</a> <span> [<a href="https://arxiv.org/pdf/1102.5700">pdf</a>, <a href="https://arxiv.org/format/1102.5700">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="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1751-8113/45/36/365206">10.1088/1751-8113/45/36/365206 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A Quantum Affine Algebra for the Deformed Hubbard Chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Galleas%2C+W">Wellington Galleas</a>, <a href="/search/math-ph?searchtype=author&query=Matsumoto%2C+T">Takuya Matsumoto</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="1102.5700v3-abstract-short" style="display: inline;"> The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.5700v3-abstract-full').style.display = 'inline'; document.getElementById('1102.5700v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.5700v3-abstract-full" style="display: none;"> The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above mentioned Yangian and to the conventional quantum affine sl(2|2) algebra in two special limits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.5700v3-abstract-full').style.display = 'none'; document.getElementById('1102.5700v3-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, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">24 pages, v2: minor amendment of (7.2), v3: accepted for publication in JPA, minor corrections</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2011-005 <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 17B37; 17B67; 81U15 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A45, 365206 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1002.1097">arXiv:1002.1097</a> <span> [<a href="https://arxiv.org/pdf/1002.1097">pdf</a>, <a href="https://arxiv.org/format/1002.1097">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="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1751-8113/44/26/265202">10.1088/1751-8113/44/26/265202 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</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="1002.1097v3-abstract-short" style="display: inline;"> The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum-deformation of the Hubbard model in the classical limit. This leads to a novel classical r-matrix of trigonometric kind. We derive the corresponding one-parameter family of Lie bialgebras as a deformation o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.1097v3-abstract-full').style.display = 'inline'; document.getElementById('1002.1097v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1002.1097v3-abstract-full" style="display: none;"> The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum-deformation of the Hubbard model in the classical limit. This leads to a novel classical r-matrix of trigonometric kind. We derive the corresponding one-parameter family of Lie bialgebras as a deformation of the affine gl(2|2) Kac-Moody superalgebra. In particular, we discuss the affine extension as well as discrete symmetries, and we scan for simpler limiting cases, such as the rational r-matrix for the undeformed Hubbard model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.1097v3-abstract-full').style.display = 'none'; document.getElementById('1002.1097v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 April, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 February, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">41 pages, v2: minor textual improvements, references added, v3: minor improvements, references added, change of convention x(v2)=h'x(v3)-ih</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2010-016 <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 17B62; 81U15; 17B67; 17B25 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.A44:265202,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0902.0956">arXiv:0902.0956</a> <span> [<a href="https://arxiv.org/pdf/0902.0956">pdf</a>, <a href="https://arxiv.org/format/0902.0956">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="Statistical Mechanics">cond-mat.stat-mech</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/10.1088/1751-8113/42/28/285205">10.1088/1751-8113/42/28/285205 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Long-Range Deformations for Integrable Spin Chains </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Bargheer%2C+T">Till Bargheer</a>, <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Loebbert%2C+F">Florian Loebbert</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="0902.0956v3-abstract-short" style="display: inline;"> We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map an… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0902.0956v3-abstract-full').style.display = 'inline'; document.getElementById('0902.0956v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0902.0956v3-abstract-full" style="display: none;"> We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest-neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0902.0956v3-abstract-full').style.display = 'none'; document.getElementById('0902.0956v3-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 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 February, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2009. </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">63 pages, v2: references added, v3: typos corrected in eqs (8.20) and (8.24)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2009-009 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.A42:285205,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0807.5081">arXiv:0807.5081</a> <span> [<a href="https://arxiv.org/pdf/0807.5081">pdf</a>, <a href="https://arxiv.org/format/0807.5081">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="Statistical Mechanics">cond-mat.stat-mech</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/10.1088/1742-5468/2008/11/L11001">10.1088/1742-5468/2008/11/L11001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Bargheer%2C+T">Till Bargheer</a>, <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Loebbert%2C+F">Florian Loebbert</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="0807.5081v3-abstract-short" style="display: inline;"> We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in recent advances in string/gauge duality. The method is based on arbitrary nearest-neighbour integrable spin chains and it sheds light on the moduli space of def… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.5081v3-abstract-full').style.display = 'inline'; document.getElementById('0807.5081v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0807.5081v3-abstract-full" style="display: none;"> We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in recent advances in string/gauge duality. The method is based on arbitrary nearest-neighbour integrable spin chains and it sheds light on the moduli space of deformation parameters. We also derive the closed chain asymptotic Bethe equations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.5081v3-abstract-full').style.display = 'none'; document.getElementById('0807.5081v3-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 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 July, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2008. </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">10 pages, v2: reference added, minor changes, v3: published version with added/updated references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2008-052 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Stat.Mech.0811:L11001,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0804.0324">arXiv:0804.0324</a> <span> [<a href="https://arxiv.org/pdf/0804.0324">pdf</a>, <a href="https://arxiv.org/format/0804.0324">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="Statistical Mechanics">cond-mat.stat-mech</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/10.1088/1367-2630/10/10/103023">10.1088/1367-2630/10/10/103023 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Stability for the Heisenberg Ferromagnet </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Bargheer%2C+T">Till Bargheer</a>, <a href="/search/math-ph?searchtype=author&query=Beisert%2C+N">Niklas Beisert</a>, <a href="/search/math-ph?searchtype=author&query=Gromov%2C+N">Nikolay Gromov</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="0804.0324v1-abstract-short" style="display: inline;"> Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it is a priori not clear whether any given admissible spectral curve can actually be realised as a solution to the discrete Bethe equations, a property which ca… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0804.0324v1-abstract-full').style.display = 'inline'; document.getElementById('0804.0324v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0804.0324v1-abstract-full" style="display: none;"> Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it is a priori not clear whether any given admissible spectral curve can actually be realised as a solution to the discrete Bethe equations, a property which can be referred to as stability. In order to study the issue of stability, we find and explore the general two-cut solution or elliptic curve. It turns out that the moduli space of this elliptic curve shows a surprisingly rich structure. We present the various cases with illustrations and thus gain some insight into the features of multi-cut solutions. It appears that all admissible spectral curves are indeed stable if the branch cuts are positioned in a suitable, non-trivial fashion. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0804.0324v1-abstract-full').style.display = 'none'; document.getElementById('0804.0324v1-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 April, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2008. </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">82 pages, a figure a page or so</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2008-010, LPTENS 08/19, SPhT-t08/051 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> New J. Phys. 10 (2008) 103023 </p> </li> </ol> <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 href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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