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. arXiv:1902.04142v1 [hep-th]

We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the λ-deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the λdeformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to "integrable" boundary configurations. We illustrate this with examples based on SU(2) and SL(2, R), and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Lie T-duality. We show that the D2 supported by D0 charge in the λ-deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the η-deformation of the principal chiral model.