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 |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| 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| _version_ | 1860006087518846976 |
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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.
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| 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. en 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 published earlier |
| 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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