4-dimensional Chern-Simons theory and integrable field theories

Lacroix, Sylvain

doi:10.48550/arxiv.2109.14278

Cited by 3 publications

(3 citation statements)

References 79 publications

(205 reference statements)

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“…In this final section we have outlined some of the many generalisations of the PCM, the PCWZM and the WZW model, their deformations and their duals. A full classification of all integrable sigma models remains an open problem, with more modern formalisms such as those based on affine Gaudin models and higher-dimensional Chern-Simons theories [72,[156][157][158] providing new insights and promising avenues to explore, as discussed in the accompanying review article 'four-dimensional Chern-Simons theory and integrable field theories' by Lacroix [159]. Such new formalisms also have the potential to help investigate the quantum physics of these models, about which much remains to be understood.…”

Section: Discussionmentioning

confidence: 99%

Integrable deformations of sigma models

Hoare

2022

J. Phys. A: Math. Theor.

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In this pedagogical review we introduce systematic approaches to deforming integrable 2-dimensional sigma models. We use the integrable principal chiral model and the conformal Wess-Zumino-Witten model as our starting points and explore their Yang-Baxter and current-current deformations. There is an intricate web of relations between these models based on underlying algebraic structures and worldsheet dualities, which is highlighted throughout. We finish with a discussion of the generalisation to other symmetric integrable models, including some original results related to ZT cosets and their deformations, and the application to string theory. This review is based on notes written for lectures delivered at the school "Integrability, Dualities and Deformations," which ran from 23 to 27 August 2021 in Santiago de Compostela and virtually.

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Section: Discussionmentioning

confidence: 99%

Integrable deformations of sigma models

Hoare

2022

J. Phys. A: Math. Theor.

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“…This paper is organized as follows. In the next section we briefly explain 4D-CS construction of 2D integrable models based on the articles [8,19]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles

2022

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We compare the construction of 2D integrable models through two gauge field theories. The first one is the 4D Chern–Simons (4D-CS) theory proposed by Costello and Yamazaki. The second one is the 2D generalization of the Hitchin integrable systems constructed by means of affine Higgs bundles (AHB). We illustrate the latter approach by considering 1 + 1 field versions of integrable systems including the Calogero–Moser field theory, the Landau–Lifshitz model and the field theory generalization of the elliptic Gaudin model.

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“…The paper is organized as follows. In the next Section we explain briefly 4d-CS construction of 2d integrable models based on the articles [2,11]. In Section 3 the AHB construction is given following notations from [12,23].…”

Section: Introductionmentioning

confidence: 99%

2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles

Levin,

Olshanetsky,

Zotov

2022

Preprint

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We compare constructions of 2d integrable models by means of two gauge field theories. The first one is the 4d Chern-Simons (4d-CS) theory proposed by Costello and Yamazaki. The second one is the 2d generalization of the Hitchin integrable systems constructed by means the Affine Higgs bundles (AHB). We illustrate the latter approach by considering 1+1 field versions of elliptic integrable systems including the Calogero-Moser field theory, the Landau-Lifshitz model and the field theory generalization of the elliptic Gaudin model.

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4-dimensional Chern-Simons theory and integrable field theories

Cited by 3 publications

References 79 publications

Integrable deformations of sigma models

Integrable deformations of sigma models

2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles

2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles

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