Institute for Mathematical Physics the Geometry of Wzw Branes the Geometry of Wzw Branes

The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string vertex operators. In the limit of large level, we nd branes whose world volume is a regular conjugacy class or, in the case of symmetry breaking boundary conditions, a `twined' version thereof. In particular, in this limit one recovers the commutative algebra of functions over the brane world volume, and open strings connecting diierent branes disappear. At nite level, the branes get smeared out, yet their approximate localization at (twined) conjugacy classes can be detected unambiguously. It is also established that in any rational conformal eld theory the structure constants of the algebra of boundary operators coincide with speciic entries of fusing matrices.