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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 058, 45 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.058
(Mi sigma1741)
 

This article is cited in 18 scientific papers (total in 18 papers)

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

Sylvain Lacroixab, Benoît Vicedoc

a Zentrum für Mathematische Physik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
b II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
c Department of Mathematics, University of York, York YO10 5DD, UK
References:
Abstract: 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 h and L, with L depending rationally on an auxiliary complex parameter, which are tied together by a constraint. When the latter can be solved for L in terms of h this produces a 2d integrable field theory for the 2d field h whose Lax connection is given by L(h). 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 E-models.
Keywords: 4d Chern–Simons theory, E-models, affine Gaudin models, integrable σ-models.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 390833306
The work of S.L. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306.
Received: December 7, 2020; in final form May 31, 2021; Published online June 10, 2021
Bibliographic databases:
Document Type: Article
MSC: 17B80, 37K05, 37K10
Language: English
Citation: Sylvain Lacroix, Benoît Vicedo, “Integrable E-Models, 4d Chern–Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects”, SIGMA, 17 (2021), 058, 45 pp.
Citation in format AMSBIB
\Bibitem{LacVic21}
\by Sylvain~Lacroix, Beno{\^\i}t~Vicedo
\paper Integrable $\mathcal{E}$-Models, $4\mathrm{d}$ Chern--Simons Theory and Affine Gaudin Models. I.~Lagrangian Aspects
\jour SIGMA
\yr 2021
\vol 17
\papernumber 058
\totalpages 45
\mathnet{http://mi.mathnet.ru/sigma1741}
\crossref{https://doi.org/10.3842/SIGMA.2021.058}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000662981100001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85110944724}
Linking options:
  • https://www.mathnet.ru/eng/sigma1741
  • https://www.mathnet.ru/eng/sigma/v17/p58
  • This publication is cited in the following 18 articles:
    1. Nathan Berkovits, Rodrigo S. Pitombo, “4D Chern-Simons and the pure spinor AdS5×S5 superstring”, Phys. Rev. D, 109:10 (2024)  crossref
    2. Sylvain Lacroix, Anders Wallberg, “Geometry of the spectral parameter and renormalisation of integrable sigma-models”, J. High Energ. Phys., 2024:5 (2024)  crossref
    3. Sylvain Lacroix, Anders Wallberg, “An elliptic integrable deformation of the Principal Chiral Model”, J. High Energ. Phys., 2024:5 (2024)  crossref
    4. Ctirad Klimčík, “Point particle E-models”, Journal of Mathematical Physics, 65:5 (2024)  crossref
    5. Lewis T. Cole, Ryan A. Cullinan, Ben Hoare, Joaquin Liniado, Daniel C. Thompson, “Integrable deformations from twistor space”, SciPost Phys., 17:1 (2024)  crossref
    6. David Osten, “Heterotic integrable deformation of the principal chiral model”, Phys. Rev. D, 109:10 (2024)  crossref
    7. Joaquin Liniado, Benoît Vicedo, “Integrable Degenerate \varvecE-Models from 4d Chern–Simons Theory”, Ann. Henri Poincaré, 24:10 (2023), 3421  crossref
    8. Roland Bittleston, David Skinner, “Twistors, the ASD Yang-Mills equations and 4d Chern-Simons theory”, J. High Energ. Phys., 2023:2 (2023)  crossref
    9. Alex S. Arvanitakis, Lewis T. Cole, Ondrej Hulik, Alexander Sevrin, Daniel C. Thompson, “Unifying approaches to chiral bosons”, Phys. Rev. D, 107:12 (2023)  crossref
    10. Tommaso Franzini, Charles Young, “Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine sl2 Gaudin model”, J. Phys. A: Math. Theor., 56:10 (2023), 105201  crossref
    11. Falk Hassler, Sylvain Lacroix, Benoît Vicedo, “The magic renormalisability of affine Gaudin models”, J. High Energ. Phys., 2023:12 (2023)  crossref
    12. Daniel Butter, Falk Hassler, Christopher N. Pope, Haoyu Zhang, “Generalized dualities and supergroups”, J. High Energ. Phys., 2023:12 (2023)  crossref
    13. Sylvain Lacroix, “On a class of conformal E-models and their chiral Poisson algebras”, J. High Energ. Phys., 2023:6 (2023)  crossref
    14. Klimcik C., “On Strong Integrability of the Dressing Cosets”, Ann. Henri Poincare, 23:7 (2022), 2545–2578  crossref  mathscinet  isi  scopus
    15. Lacroix S., “Four-Dimensional Chern-Simons Theory and Integrable Field Theories”, J. Phys. A-Math. Theor., 55:8 (2022), 083001  crossref  mathscinet  isi  scopus
    16. Fukushima O., Sakamoto J.-i., Yoshida K., “Non-Abelian Toda Field Theories From a 4D Chern-Simons Theory”, J. High Energy Phys., 2022, no. 3, 158  crossref  mathscinet  isi  scopus
    17. Osamu Fukushima, Jun-ichi Sakamoto, Kentaroh Yoshida, “Integrable deformed T1,1 sigma models from 4D Chern-Simons theory”, J. High Energ. Phys., 2021:9 (2021)  crossref
    18. Falk Hassler, Thomas B. Rochais, “O(D,D)-covariant two-loop β-functions and Poisson-Lie T-duality”, J. High Energ. Phys., 2021:10 (2021)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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