Integrable λ-deformations of the Euclidean black string

Abstract

Non-trivial outer algebra automorphisms may be utilized in λ-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT SU(2)k×U(1)/U(1)q with a vector and axial residual gauge. Besides the integer level k and the deformation parameter λ, these models are characterized by the embedding parameter q of the U(1) factor. We show that an axial-vector T-duality persists along the deformations and, therefore, the models are canonically equivalent. We demonstrate integrability even though the space is non-symmetric and compute the RG-flow equations for the parameters λ and q. Our example provides an integrable deformation of the gravitational solution representing a Euclidean three-dimensional black string.