A bound on the entropy of supergravity?

TL;DR

This paper compares two methods of counting BPS states in supergravity with fixed D4D0 charge, finding that supergravity alone underestimates the total black hole entropy and that a unitarity bound emerges from classical supergravity dynamics.

Contribution

It provides a detailed comparison of state counts from multicentered solutions and supergravity excitations, revealing limitations of supergravity in capturing black hole microstates.

Findings

Leading degeneracies match in large charge limit

Supergravity states are parametrically fewer than black hole entropy

Stringy exclusion principle bound appears in supergravity dynamics

Abstract

We determine, in two independent ways, the number of BPS quantum states arising from supergravity 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 consisting of anti-D0-branes bound to a D6-anti-D6 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 black holes. Comparing the free supergravity calculation to that of the D6-anti-D6-D0 system we find that the bound on the free spectrum imposed by the stringy exclusion principle (a unitarity bound in the dual CFT) seems to be captured in the dynamics of the fully interacting but classcial supergravity equations of motion.