Holomorphic Chern-Simons theory and affine Gaudin models

Abstract

We relate two formalisms recently proposed for describing classical integrable field theories. The first is based on the action of four-dimensional holomorphic Chern-Simons theory introduced and studied by Costello, Witten and Yamazaki. The second makes use of classical generalised Gaudin models associated with untwisted affine Kac-Moody algebras.

arXiv comment18 pages, v2: minor typos corrected and references added

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Cited by in corpus (11)

• Integrable Deformations of Sigma Models
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Comments on $\eta$-deformed principal chiral model from 4D Chern-Simons theory
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Deformed Integrable Models from Holomorphic Chern-Simons Theory
• $\lambda$-deformed $Ad{S}_5\times S^5$ superstring from 4D Chern-Simons theory
• Resurgence in the Bi-Yang-Baxter Model
• Kondo line defects and affine Gaudin models
• Four-Dimensional Chern-Simons and Gauged Sigma Models