Non-trivial outer algebra automorphisms may be utilized inλ-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 CFTSU(2)k×U(1)/U(1)qwith a vector and axial residual gauge. Besides the integer levelkand the deformation parameterλ, these models are characterized by the embedding parameterqof theU(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 theRG-flow equations for the parametersλandq. Our example provides an integrable deformation of the gravitational solution representing a Euclidean three-dimensional black string.
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