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arXiv · 2311.09301

An elliptic integrable deformation of the Principal Chiral Model

Sylvain Lacroix·Anders Wallberg
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Abstract

We introduce a new elliptic integrable $\sigma$-model in the form of a two-parameter deformation of the Principal Chiral Model on the group $\text{SL}_{\mathbb{R}}(N)$, generalising a construction of Cherednik for $N=2$ (up to reality conditions). We exhibit the Lax connection and $\mathcal{R}$-matrix of this theory, which depend meromorphically on a spectral parameter valued in the torus. Furthermore, we explain the origin of this model from an equivariant semi-holomorphic 4-dimensional Chern-Simons theory on the torus. This approach opens the way for the construction of a large class of elliptic integrable $\sigma$-models, with the deformed Principal Chiral Model as the simplest example.

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Sylvain Lacroix, Anders Wallberg. 2023-11-15. An elliptic integrable deformation of the Principal Chiral Model. https://doi.org/10.1007/jhep05(2024)006

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