Integrable deformations of coupled sigma-models

Abstract

We construct integrability-preserving deformations of the integrable $\sigma$-model coupling together $N$ copies of the Principal Chiral Model. These deformed theories are obtained using the formalism of affine Gaudin models, by applying various combinations of Yang-Baxter and $\lambda$-deformations to the different copies of the undeformed model. We describe these models both in the Hamiltonian and Lagrangian formulation and give explicit expressions of their action and Lax pair. In particular, we recover through this construction various integrable $\lambda$-deformed models previously introduced in the literature. Finally, we discuss the relation of the present work with the semi-homolomorphic four-dimensional Chern-Simons theory.

arXiv comment49 pages ; references added, some changes in the presentation ; published version

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Cited by in corpus (14)

• Integrable Deformations of Sigma Models
• 4-dimensional Chern-Simons theory and integrable field theories
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• RG flows of integrable $\sigma$-models and the twist function
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
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• Deformed Integrable Models from Holomorphic Chern-Simons Theory
• Universal 1-loop divergences for integrable sigma models
• Integrable Deformations from Twistor Space
• 3-dimensional mixed BF theory and Hitchin's integrable system
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude