A bound on the entropy of supergravity?

We determine, in two independent ways, the number of BPS quantum states arising from supergracity degrees of freedom in a system with fixed total D4D0 charge. First, we count states generated by quantizing the spacetime degrees of freedom of entropyless multicentered solutions consistinf of (D0) over bar -branes bound to a D6 (D6) over bar pair. Second, we determine the number of free supergravity excitations of the corresponding AdS(3) geometry with the same total charge. We find that, although these two approaches yield a priori different sets of states, the leading degeneracies in a large charge expansion are equal to each other and that, furthermore, the number of such states is parametrically smaller than that arising from the D4D0 black hole's entropy. This strongly suggests that supergravity alone is not sufficient to capture all degrees of freedom of large supersymmetric balck holes. Comparing the free supergracity calculatioj to that of the D6 (D6) over bar D0 system we find that the bound on the free spectrum imposed by the stringy exclusion principle (a unitarity bound in the dual CFT) seem to be captured in the dynamics of the fully interacting but classical supergravity equations of motion.