A bound on the entropy of supergravity?

TL;DR

The work analyzes a BPS subsector of D4D0 black hole microstates by quantizing backreacted D6–D̄6–D0 multicenter solutions and by counting free supergravity excitations in AdS3×S2 with the same total charge. It shows that the leading growth of these supergravity-derived degeneracies matches across the two methods but remains exponentially smaller than the D4D0 black hole entropy, implying essential non-supergravity degrees of freedom for typical black hole microstates. A stringy exclusion principle bound emerges naturally in the interacting supergravity dynamics, linking gravitational constraints to CFT unitarity bounds. The results offer a precise bound on the part of the black hole spectrum accessible to supergravity and provide insights into the role of microstate geometries and macroscopic quantum fluctuations in AdS/CFT. The study also highlights phase-transition-like behavior in the halo counting and emphasizes that fully generic microstates likely require string or brane degrees of freedom beyond supergravity.

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.