Homogeneous Yang–Baxter deformations as non-abelian duals of the AdS5 σ-model

Abstract

We propose that the Yang–Baxter deformation of the symmetric space σ-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 σ-model. The same should also be true for the full 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 model by a combination of T-dualities and nonlinear 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.