Yang-Baxter $\sigma$-models and dS/AdS T-duality

TL;DR

This paper explores nonlinear sigma-models with specific symmetries on group manifolds and examines their T-duality properties, including examples involving de Sitter space and WZW models, revealing new duality relationships.

Contribution

It identifies new classes of sigma-models with symmetric and Poisson-Lie symmetries and analyzes their T-duality, especially in the context of de Sitter space and WZW models.

Findings

Existence of nonlinear sigma-models with left symmetric and right Poisson-Lie symmetry.

Detailed analysis of T-duality in anisotropic principal chiral models.

Identification of de Sitter space as a non-Abelian T-dual in WZW models.

Abstract

We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic principal chiral model and the $SL(2,C)/SU(2)$ WZW model. The latter has the de Sitter space as its (conformal) non-Abelian dual.