Free Field Realization of D-brane in Group Manifold

We construct the boundary state for the D-brane in the SU(2) group manifold directly in terms of the group variables. We propose a matching condition for the left- and the right-moving sectors including the zero modes that describes a D-brane of the Neumann-type. The free field realization of the WZW model is used to obtain the boundary state subject to the matching condition. We show that the resulting state coincides with Cardy’s state. The structure of the BRST cohomology is realized by imposing the invariance of the state under the Weyl group of the current algebra.