A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory

Abstract

In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern-Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable $\sigma$-models which are known to admit descriptions as affine Gaudin models. This includes both the Yang-Baxter deformation and the $\lambda$-deformation of the principal chiral model. We also give an interpretation of Poisson-Lie $T$-duality in this setting and derive the action of the $\mathsf{E}$-model.

37 pages

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Cited by in corpus (37)

• 4-dimensional Chern-Simons theory and integrable field theories
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• 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
• Integrable Kondo problems
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• RG flows of integrable $\sigma$-models and the twist function
• Sigma models with local couplings: a new integrability -- RG flow connection
• Integrable deformations of coupled sigma-models
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• 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
• Universal 1-loop divergences for integrable sigma models
• Integrable Deformations from Twistor Space
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• An elliptic integrable deformation of the Principal Chiral Model
• Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• Q-operators are 't Hooft lines
• Higher Gauge Theory and Integrability
• 4D Chern-Simons theory with auxiliary fields
• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• Superspin Chains Solutions from 4D Chern-Simons Theory
• The Courant-Hilbert construction in 4D Chern-Simons theory
• 3-dimensional mixed BF theory and Hitchin's integrable system
• Integrability in Gravity from Chern-Simons Theory
• Integrability of the $\lambda$-deformation of the PCM with spectators
• A generalized 4d Chern-Simons theory
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Four-Dimensional Chern-Simons and Gauged Sigma Models
• Contact 4d Chern-Simons theory: Generalities
• Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory
• Integrable models from 4d holomorphic BF theory