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Folded quantum integrable models and deformed W-algebras

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the Bethe Ansatz equations of the standard integrable model asso...

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Detalles Bibliográficos
Autores principales: Frenkel, Edward, Hernandez, David, Reshetikhin, Nicolai
Lenguaje:eng
Publicado: 2021
Materias:
Acceso en línea:http://cds.cern.ch/record/2789021
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author Frenkel, Edward
Hernandez, David
Reshetikhin, Nicolai
author_facet Frenkel, Edward
Hernandez, David
Reshetikhin, Nicolai
author_sort Frenkel, Edward
collection CERN
description We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the Bethe Ansatz equations of the standard integrable model associated to the quantum affine algebra $U_q(\widehat{\mathfrak g'})$ of the simply-laced Lie algebra ${\mathfrak g}'$ corresponding to ${\mathfrak g}$. Our construction is motivated by the analysis of the second classical limit of the deformed ${\mathcal W}$-algebra of ${\mathfrak g}$, which we interpret as a "folding" of the Grothendieck ring of finite-dimensional representations of $U_q(\widehat{\mathfrak g'})$. We conjecture, and verify in a number of cases, that the spaces of states of the folded integrable model can be identified with finite-dimensional representations of $U_q({}^L\widehat{\mathfrak g})$, where $^L\widehat{\mathfrak g}$ is the (twisted) affine Kac-Moody algebra Langlands dual to $\widehat{\mathfrak g}$. We discuss the analogous structures in the Gaudin model which appears in the limit $q \to 1$. Finally, we describe a conjectural construction of the simple ${\mathfrak g}$-crystals in terms of the folded $q$-characters.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2021
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spelling cern-27890212021-12-17T09:00:53Zhttp://cds.cern.ch/record/2789021engFrenkel, EdwardHernandez, DavidReshetikhin, NicolaiFolded quantum integrable models and deformed W-algebrasnlin.SINonlinear Systemsmath.RTMathematical Physics and Mathematicsmath.AGMathematical Physics and Mathematicshep-thParticle Physics - Theorymath.QAMathematical Physics and MathematicsWe propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the Bethe Ansatz equations of the standard integrable model associated to the quantum affine algebra $U_q(\widehat{\mathfrak g'})$ of the simply-laced Lie algebra ${\mathfrak g}'$ corresponding to ${\mathfrak g}$. Our construction is motivated by the analysis of the second classical limit of the deformed ${\mathcal W}$-algebra of ${\mathfrak g}$, which we interpret as a "folding" of the Grothendieck ring of finite-dimensional representations of $U_q(\widehat{\mathfrak g'})$. We conjecture, and verify in a number of cases, that the spaces of states of the folded integrable model can be identified with finite-dimensional representations of $U_q({}^L\widehat{\mathfrak g})$, where $^L\widehat{\mathfrak g}$ is the (twisted) affine Kac-Moody algebra Langlands dual to $\widehat{\mathfrak g}$. We discuss the analogous structures in the Gaudin model which appears in the limit $q \to 1$. Finally, we describe a conjectural construction of the simple ${\mathfrak g}$-crystals in terms of the folded $q$-characters.arXiv:2110.14600oai:cds.cern.ch:27890212021-10-27
spellingShingle nlin.SI
Nonlinear Systems
math.RT
Mathematical Physics and Mathematics
math.AG
Mathematical Physics and Mathematics
hep-th
Particle Physics - Theory
math.QA
Mathematical Physics and Mathematics
Frenkel, Edward
Hernandez, David
Reshetikhin, Nicolai
Folded quantum integrable models and deformed W-algebras
title Folded quantum integrable models and deformed W-algebras
title_full Folded quantum integrable models and deformed W-algebras
title_fullStr Folded quantum integrable models and deformed W-algebras
title_full_unstemmed Folded quantum integrable models and deformed W-algebras
title_short Folded quantum integrable models and deformed W-algebras
title_sort folded quantum integrable models and deformed w-algebras
topic nlin.SI
Nonlinear Systems
math.RT
Mathematical Physics and Mathematics
math.AG
Mathematical Physics and Mathematics
hep-th
Particle Physics - Theory
math.QA
Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2789021
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AT hernandezdavid foldedquantumintegrablemodelsanddeformedwalgebras
AT reshetikhinnicolai foldedquantumintegrablemodelsanddeformedwalgebras