A bound on the entropy of supergravity?

• Published in: The journal of high energy physics 2010-02, Vol.2010 (2), Article 62
• Main Authors: de Boer, Jan, El-Showk, Sheer, Messamah, Ilies, Van den Bleeken, Dieter
• Format: Article
• Language: English
• Subjects: Black holes; Branes; Classical and Quantum Gravitation; Counting; Degrees of freedom; Elementary Particles; Entropy; Equations of motion; High energy physics; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Supergravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2010)062

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 -branes bound to a 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 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.