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
Article

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 \( \overline {\text{D0}} \)-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.

Keywords

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

References

  1. [1]
    J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N = 2 multicenter solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [SPIRES].CrossRefGoogle Scholar
  3. [3]
    F. Denef, On the correspondence between D-branes and stationary supergravity solutions of type-II Calabi-Yau compactifications, hep-th/0010222 [SPIRES].
  4. [4]
    B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, hep-th/0304094 [SPIRES].
  5. [5]
    I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    J. de Boer, F. Denef, S. El-Showk, I. Messamah and D. Van den Bleeken, Black hole bound states in AdS 3 × S 2 , JHEP 11 (2008) 050 [arXiv:0802.2257] [SPIRES].CrossRefGoogle Scholar
  8. [8]
    J.M. Maldacena and A. Strominger, AdS 3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  10. [10]
    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [SPIRES].CrossRefMathSciNetGoogle Scholar
  11. [11]
    K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [SPIRES].
  13. [13]
    V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black holes as effective geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    I. Bena, N. Bobev, C. Ruef and N.P. Warner, Entropy enhancement and black hole microstates, arXiv:0804.4487 [SPIRES].
  15. [15]
    D. Gaiotto, A. Strominger and X. Yin, Superconformal black hole quantum mechanics, JHEP 11 (2005) 017 [hep-th/0412322] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    S. Kim and J. Raeymaekers, Superconformal quantum mechanics of small black holes, JHEP 08 (2005) 082 [hep-th/0505176] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    F. Denef, D. Gaiotto, A. Strominger, D. Van den Bleeken and X. Yin, Black hole deconstruction, hep-th/0703252 [SPIRES].
  18. [18]
    E.G. Gimon and T.S. Levi, Black ring deconstruction, JHEP 04 (2008) 098 [arXiv:0706.3394] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  19. [19]
    T. Levi et al., Gödel space from wrapped M2-branes, JHEP 01 (2010) 001 [arXiv:0909.4081] [SPIRES].Google Scholar
  20. [20]
    I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [SPIRES].
  22. [22]
    I. Bena, C.-W. Wang and N.P. Warner, Plumbing the abyss: black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    F. Denef, Supergravity ows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    J. Raeymaekers, Near-horizon microstates of the D1-D5-P black hole, JHEP 02 (2008) 006 [arXiv:0710.4912] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  26. [26]
    I. Bena, N. Bobev, C. Ruef and N.P. Warner, Supertubes in bubbling backgrounds: Born-Infeld meets supergravity, JHEP 07 (2009) 106 [arXiv:0812.2942] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    V. Balasubramanian, E.G. Gimon and T.S. Levi, Four dimensional black hole microstates: from D-branes to spacetime foam, JHEP 01 (2008) 056 [hep-th/0606118] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    F. Larsen, The perturbation spectrum of black holes in N = 8 supergravity, Nucl. Phys. B 536 (1998) 258 [hep-th/9805208] [SPIRES].CrossRefADSGoogle Scholar
  29. [29]
    J. de Boer, Six-dimensional supergravity on S 3 × AdS 3 and 2D conformal field theory, Nucl. Phys. B 548 (1999) 139 [hep-th/9806104] [SPIRES].ADSGoogle Scholar
  30. [30]
    W. Lerche, C. Vafa and N.P. Warner, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B 324 (1989) 427 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  31. [31]
    A. Fujii, R. Kemmoku and S. Mizoguchi, D = 5 simple supergravity on AdS 3 × S 2 and N = 4 superconformal field theory, Nucl. Phys. B 574 (2000) 691 [hep-th/9811147] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  32. [32]
    D. Kutasov, F. Larsen and R.G. Leigh, String theory in magnetic monopole backgrounds, Nucl. Phys. B 550 (1999) 183 [hep-th/9812027] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    D. Gaiotto, A. Strominger and X. Yin, From AdS 3/CFT 2 to black holes/topological strings, JHEP 09 (2007) 050 [hep-th/0602046] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  34. [34]
    P. Kraus, Lectures on black holes and the AdS 3/CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [SPIRES].MathSciNetGoogle Scholar
  35. [35]
    J. de Boer, Large-N elliptic genus and AdS/CFT correspondence, JHEP 05 (1999) 017 [hep-th/9812240] [SPIRES].CrossRefGoogle Scholar
  36. [36]
    V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Inv. Math. 67 (1982) 515.MATHCrossRefMathSciNetADSGoogle Scholar

Copyright information

© 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.

Personalised recommendations