Open strings and D-branes in WZNW models

An abundance of Poisson-Lie symmetries of the WZNW models is uncovered. They give rise, via the Poisson-Lie T-duality, to a rich structure of dual pairs of D-branes configurations in group manifolds, The D-branes are characterized by their shapes and certain two-forms living on them. The WZNW path integral for the interacting D-branes diagrams is unambiguously defined if the two-form on the D-brane and the WZNW three-form on the group form an integer-valued cocycle in the relative singular cohomology of the group manifold with respect to its D-brane submanifold. An example of the SU(N) WZNW model is studied in some detail. (C) 1997 Published by Elsevier Science B.V.