Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects

We construct the actions of a very broad family of 2d integrable σ-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This 2d action depends on a pair of 2d fields and , with depending rat...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2021
Main Authors: Lacroix, Sylvain, Vicedo, Benoît
Format: Article
Language:English
Published: Інститут математики НАН України 2021
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211365
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects. Sylvain Lacroix and Benoît Vicedo. SIGMA 17 (2021), 058, 45 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Lacroix, Sylvain
Vicedo, Benoît
author_facet Lacroix, Sylvain
Vicedo, Benoît
citation_txt Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects. Sylvain Lacroix and Benoît Vicedo. SIGMA 17 (2021), 058, 45 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We construct the actions of a very broad family of 2d integrable σ-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This 2d action depends on a pair of 2d fields and , with depending rationally on an auxiliary complex parameter, which are tied together by a constraint. When the latter can be solved for in terms of , this produces a 2d integrable field theory for the 2d field h whose Lax connection is given by (). We construct a general class of solutions to this constraint and show that the resulting 2d integrable field theories can all naturally be described as -models.
first_indexed 2026-03-18T13:20:34Z
format Article
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id nasplib_isofts_kiev_ua-123456789-211365
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-18T13:20:34Z
publishDate 2021
publisher Інститут математики НАН України
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spelling Lacroix, Sylvain
Vicedo, Benoît
2025-12-30T15:56:53Z
2021
Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects. Sylvain Lacroix and Benoît Vicedo. SIGMA 17 (2021), 058, 45 pages
1815-0659
2020 Mathematics Subject Classification: 17B80; 37K05; 37K10
arXiv:2011.13809
https://nasplib.isofts.kiev.ua/handle/123456789/211365
https://doi.org/10.3842/SIGMA.2021.058
We construct the actions of a very broad family of 2d integrable σ-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This 2d action depends on a pair of 2d fields and , with depending rationally on an auxiliary complex parameter, which are tied together by a constraint. When the latter can be solved for in terms of , this produces a 2d integrable field theory for the 2d field h whose Lax connection is given by (). We construct a general class of solutions to this constraint and show that the resulting 2d integrable field theories can all naturally be described as -models.
S.L. would like to thank B. Hoare for useful discussions. The work of S.L. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy EXC 2121 Quantum Universe 390833306.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
Article
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spellingShingle Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
Lacroix, Sylvain
Vicedo, Benoît
title Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
title_full Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
title_fullStr Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
title_full_unstemmed Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
title_short Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
title_sort integrable -models, 4d chern-simons theory and affine gaudin models. i. lagrangian aspects
url https://nasplib.isofts.kiev.ua/handle/123456789/211365
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