  We consider a low-energy effective action for the gauge field on
Wess-Zumino-Witten D-branes in a compact simple Lie group, in the limit of
large k. We prove that the effective action is bounded from below, and study
stability of various D-brane configurations, including some class of
non-maximally symmetric ones. We show that for Lie groups of rank higher than
one, the D-brane ground state breaks the Kac-Moody symmetry of the boundary
theory. We then give arguments hinting that the "fuzzy sphere" D2-brane which
is known to be the stable brane configuration in the case of SU(2), may also
correspond to the ground state in other compact simple Lie groups.
