Journal of High Energy Physics

, 2011:62 | Cite as

New D1-D5-P geometries from string amplitudes

Article

Abstract

We derive the long range supergravity fields sourced by a D1-D5-P bound state from disk amplitudes for massless closed string emission. We suggest that since the parameter controlling the string perturbation expansion for this calculation decreases with distance from the bound state, the resulting asymptotic fields are valid even in the regime of parameters in which there is a classical black hole solution with the same charges. The supergravity fields differ from the black hole solution by multipole moments and are more general than those contained within known classes of solutions in the literature, whilst still preserving four supersymmetries. Our results support the conjecture that the black hole solution should be interpreted as a coarse-grained description rather than an exact description of the gravitational field sourced by D1-D5-P bound states in this regime of parameters.

Keywords

Black Holes in String Theory D-branes Conformal Field Models in String Theory 

References

  1. [1]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].MathSciNetADSGoogle Scholar
  2. [2]
    C.G. Callan and J.M. Maldacena, D-brane approach to black hole quantum mechanics, Nucl. Phys. B 472 (1996) 591 [hep-th/9602043] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    S.D. Mathur, The Fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [INSPIRE].
  5. [5]
    K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    B.D. Chowdhury and A. Virmani, Modave lectures on fuzzballs and emission from the D1-D5 system, arXiv:1001.1444 [INSPIRE].
  8. [8]
    S. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    S. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    S.D. Mathur, The Information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    S.D. Mathur and C.J. Plumberg, Correlations in Hawking radiation and the infall problem, JHEP 09 (2011) 093 [arXiv:1101.4899] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    S.D. Mathur, What the information paradox is not, arXiv:1108.0302 [INSPIRE].
  13. [13]
    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    A. Dabholkar, J.P. Gauntlett, J.A. Harvey and D. Waldram, Strings as solitons and black holes as strings, Nucl. Phys. B 474 (1996) 85 [hep-th/9511053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    C.G. Callan, J.M. Maldacena and A.W. Peet, Extremal black holes as fundamental strings, Nucl. Phys. B 475 (1996) 645 [hep-th/9510134] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    M. Taylor, General 2 charge geometries, JHEP 03 (2006) 009 [hep-th/0507223] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    I. Bena and N.P. Warner, One ring to rule them all and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].MathSciNetMATHGoogle Scholar
  21. [21]
    I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].MathSciNetADSGoogle Scholar
  22. [22]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    I. Bena, C.-W. Wang and N.P. Warner, The foaming three-charge black hole, Phys. Rev. D 75 (2007) 124026 [hep-th/0604110] [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    I. Bena, C.-W. Wang and N.P. Warner, Plumbing the abyss: black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    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] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    I. Bena, N. Bobev, S. Giusto, C. Ruef and N.P. Warner, An infinite-dimensional family of black-hole microstate geometries, JHEP 03 (2011) 022 [arXiv:1006.3497] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, A bound on the entropy of supergravity?, JHEP 02 (2010) 062 [arXiv:0906.0011] [INSPIRE].CrossRefGoogle Scholar
  29. [29]
    K. Skenderis and M. Taylor, Anatomy of bubbling solutions, JHEP 09 (2007) 019 [arXiv:0706.0216] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    S. Giusto and S.D. Mathur, Geometry of D1-D5-P bound states, Nucl. Phys. B 729 (2005) 203 [hep-th/0409067] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    J. Ford, S. Giusto and A. Saxena, A class of BPS time-dependent 3-charge microstates from spectral flow, Nucl. Phys. B 790 (2008) 258 [hep-th/0612227] [INSPIRE].MathSciNetADSGoogle Scholar
  33. [33]
    I. Bena, B.D. Chowdhury, J. de Boer, S. El-Showk and M. Shigemori, Moulting black holes, arXiv:1108.0411 [INSPIRE].
  34. [34]
    P. Di Vecchia et al., Classical p-branes from boundary state, Nucl. Phys. B 507 (1997) 259 [hep-th/9707068] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Di Vecchia, M. Frau, A. Lerda and A. Liccardo, (F, D p) bound states from the boundary state, Nucl. Phys. B 565 (2000) 397 [hep-th/9906214] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Giusto, J.F. Morales and R. Russo, D1-D5 microstate geometries from string amplitudes, JHEP 03 (2010) 130 [arXiv:0912.2270] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    S.R. Das and S.D. Mathur, Excitations of D strings, entropy and duality, Phys. Lett. B 375 (1996) 103 [hep-th/9601152] [INSPIRE].MathSciNetADSGoogle Scholar
  38. [38]
    Y. Hikida, H. Takayanagi and T. Takayanagi, Boundary states for D-branes with traveling waves, JHEP 04 (2003) 032 [hep-th/0303214] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    J.D. Blum, Gravitational radiation from traveling waves on D strings, Phys. Rev. D 68 (2003) 086003 [hep-th/0304173] [INSPIRE].ADSGoogle Scholar
  40. [40]
    C.P. Bachas and M.R. Gaberdiel, World sheet duality for D-branes with travelling waves, JHEP 03 (2004) 015 [hep-th/0310017] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  41. [41]
    W. Black, R. Russo and D. Turton, The supergravity fields for a D-brane with a travelling wave from string amplitudes, Phys. Lett. B 694 (2010) 246 [arXiv:1007.2856] [INSPIRE].MathSciNetADSGoogle Scholar
  42. [42]
    V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    V. Periwal and O. Tafjord, D-brane recoil, Phys. Rev. D 54 (1996) 3690 [hep-th/9603156] [INSPIRE].MathSciNetADSGoogle Scholar
  44. [44]
    I.I. Kogan, N.E. Mavromatos and J.F. Wheater, D-brane recoil and logarithmic operators, Phys. Lett. B 387 (1996) 483 [hep-th/9606102] [INSPIRE].MathSciNetADSGoogle Scholar
  45. [45]
    I.I. Kogan and J.F. Wheater, Boundary logarithmic conformal field theory, Phys. Lett. B 486 (2000) 353 [hep-th/0003184] [INSPIRE].MathSciNetADSGoogle Scholar
  46. [46]
    N.D. Lambert, H. Liu and J.M. Maldacena, Closed strings from decaying D-branes, JHEP 03 (2007) 014 [hep-th/0303139] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    I. Bena, J. de Boer, M. Shigemori and N.P. Warner, Double, double supertube bubble, JHEP 10 (2011) 116 [arXiv:1107.2650] [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The library of Babel: on the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [INSPIRE].ADSGoogle Scholar
  49. [49]
    V. Balasubramanian, B. Czech, K. Larjo and J. Simon, Integrability versus information loss: a simple example, JHEP 11 (2006) 001 [hep-th/0602263] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  50. [50]
    V. Balasubramanian, B. Czech, K. Larjo, D. Marolf and J. Simon, Quantum geometry and gravitational entropy, JHEP 12 (2007) 067 [arXiv:0705.4431] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    C.G. Callan Jr., C. Lovelace, C. Nappi and S. Yost, Loop corrections to superstring equations of motion, Nucl. Phys. B 308 (1988) 221 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  52. [52]
    C. Bachas, Relativistic string in a pulse, Annals Phys. 305 (2003) 286 [hep-th/0212217] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  53. [53]
    M. Bertolini, M. Billó, A. Lerda, J.F. Morales and R. Russo, Brane world effective actions for D-branes with fluxes, Nucl. Phys. B 743 (2006) 1 [hep-th/0512067] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    H. Liu, G.W. Moore and N. Seiberg, Strings in a time dependent orbifold, JHEP 06 (2002) 045 [hep-th/0204168] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    H. Liu, G.W. Moore and N. Seiberg, Strings in time dependent orbifolds, JHEP 10 (2002) 031 [hep-th/0206182] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  56. [56]
    M. Billó et al., Classical gauge instantons from open strings, JHEP 02 (2003) 045 [hep-th/0211250] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    M. Billó, M. Frau, L. Giacone and A. Lerda, Holographic non-perturbative corrections to gauge couplings, JHEP 08 (2011) 007 [arXiv:1105.1869] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    J. Polchinski, String theory. Volume 2: superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998).Google Scholar
  59. [59]
    O. Bergman and B. Zwiebach, The dilaton theorem and closed string backgrounds, Nucl. Phys. B 441 (1995) 76 [hep-th/9411047] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  60. [60]
    M. Billó et al., Microscopic string analysis of the D0-D8-brane system and dual R-R states, Nucl. Phys. B 526 (1998) 199 [hep-th/9802088] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Dipartimento di Fisica “Galileo Galilei”Università di PadovaPadovaItaly
  2. 2.INFN, Sezione di PadovaPadovaItaly
  3. 3.Centre for Research in String Theory, School of PhysicsQueen Mary University of LondonLondonUK
  4. 4.Department of PhysicsThe Ohio State UniversitColumbusUSA

Personalised recommendations