SU(2) WZW D-branes and quantized worldvolume U(1) flux on S²

We discuss possible D-brane configurations on SU(2) group manifolds in the sigma model approach. When we turn the boundary conditions of the spacetime fields into the boundary gluing conditions of chiral currents, we find that for all D-branes except the spherical D2-branes, the gluing matrices R^a_{b} depend on the fields, so the chiral Kac-Moody symmetry is broken, but conformal symmetry is maintained. Matching the spherical D2-branes derived from the sigma model with those from the boundary state approach we obtain a U(1) field strength that is consistent with flux quantization.