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We construct integrable deformations of the λ-type for asymmetrically gauged WZW models. This is achieved by a modification of the Sfetsos gauging procedure to account for a possible automorphism that is allowed in G/G models. We verify classical integrability, derive the one-loop beta function for the deformation parameter and give the construction of integrable D-brane configurations in these models. As an application, we detail the case of the λ-deformation of the cigar geometry corresponding to the axial gauged SL(2, R)/U(1) theory at large k. Here we also exhibit a range of both A-type and B-type integrability preserving D-brane configurations.
Bibliographical note25 pages, 1 figure