Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model

TL;DR

This paper shows that homogeneous Yang-Baxter deformations of the AdS_5 sigma-model are equivalent to non-abelian duals of the undeformed model, generalizing recent observations and including TsT transformations as special cases.

Contribution

It establishes a general equivalence between homogeneous Yang-Baxter deformations and non-abelian duals for AdS_5 models, extending to supercosets and TsT transformations.

Findings

Homogeneous Yang-Baxter deformations are equivalent to non-abelian duals.

Explicit examples in AdS_5 sigma-model demonstrate the equivalence.

TsT transformations are special cases of non-abelian duals.

Abstract

We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.