The geometry of WZW branes

The structures in target space geometry that correspond to conformally inva riant boundary conditions in WZW theories are determined both by studying t he scattering of closed string states and by investigating the algebra of o pen string vertex operators. In the limit of large level, we find branes wh ose world volume is a regular conjugacy class or, in the case of symmetry b reaking 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 different branes disappear. At f inite 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 field theory the stru cture constants of the algebra of boundary operators coincide with specific entries of fusing matrices. (C) 2000 Elsevier Science B.V. All rights rese rved. MSC 81T40: 81T30: 81R10.