Journal of High Energy Physics

, 2010:62 | Cite as

A bound on the entropy of supergravity?

  • Jan de Boer
  • Sheer El-Showk
  • Ilies Messamah
  • Dieter Van den Bleeken
Open Access


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 \( \overline {\text{D0}} \)-branes bound to a D6\( \overline {\text{D6}} \) pair. Second, we determine the number of free supergravity excitations of the corresponding AdS3 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\( \overline {\text{D6}} \)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.


Black Holes in String Theory AdS-CFT Correspondence D-branes 


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© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Jan de Boer
    • 1
  • Sheer El-Showk
    • 1
  • Ilies Messamah
    • 1
  • Dieter Van den Bleeken
    • 2
  1. 1.Instituut voor Theoretische FysicaUniversiteit AmsterdamAmsterdamThe Netherlands
  2. 2.NHETC and Department of Physics and AstronomyRutgers UniversityPiscatawayU.S.A.

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