Constrained affine Gaudin models and diagonal Yang-Baxter deformations

Abstract

We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging procedure which allows to reformulate the non-constrained realisations of affine Gaudin models considered recently in [JHEP 06 (2019) 017] as equivalent models with a gauge symmetry. This reformulation is then used to construct integrable deformations of these models breaking their diagonal symmetry. In a second time, we apply these general methods to the integrable coupled $\sigma$-model introduced recently, whose target space is the N-fold Cartesian product $G_0^N$ of a real semi-simple Lie group $G_0$. We present its gauged formulation as a model on $G_0^{N+1}$ with a gauge symmetry acting as the right multiplication by the diagonal subgroup $G_0^{\text{diag}}$ and construct its diagonal homogeneous Yang-Baxter deformation.

95 pages

References in corpus (5)

• Non-local charges, Zm gradings and coset space actions
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Assembling integrable sigma-models as affine Gaudin models
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Integrable coupled sigma-models

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