D-branes (or not) in the non-Abelian T-dual of the SU(2) WZW model

Following on from a previous article [1], we consider open strings in the non-Abelian T-dual of the SU(2)k WZW model, with respect to the vector SU(2) isometry. Since in this case the dual theory has an exact CFT description, we look at the chiral algebra-preserving D-branes. The general conclusion is that a large set of branes, while consistent boundary conditions on the worldsheet, are sent to infinity in the target space. This suggests inconsistency of the strict non-Abelian duality with open strings, in this case.