Branes in the GL(1|1)GL(1|1) WZNW model

We initiate a systematic study of boundary conditions in conformal field theories with target space supersymmetry. The WZNW model on GL(1|1)GL(1|1) is used as a prototypical example for which we find the complete set of maximally symmetric branes. This includes a unique brane of maximal super-dimension 2|22|2, a 2-parameter family of branes with super-dimension 0|20|2 and an infinite set of fully localized branes possessing a single modulus. Members of the latter family can only exist along certain lines on the bosonic base, much like fractional branes at orbifold singularities. Our results establish that all essential algebraic features of Cardy-type boundary theories carry over to the non-rational logarithmic WZNW model on GL(1|1)GL(1|1).