D-branes in λ-deformations

We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the lambda-deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the lambda-deformed 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 lambda-deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the lambda-deformation of the principal chiral model.