Download PDF

Black holes and fourfolds

Open Access
Article
First Online:
Received:
Accepted:

Abstract

We establish a relation between the structure governing four- and five- dimensional black holes and multicenter solutions on the one hand and Calabi-Yau flux compactifications of M-theory and type IIB string theory on the other hand, for both supersymmetric and non-supersymmetric solutions. We find that the known BPS and almost-BPS multicenter black hole solutions can be interpreted as GKP compactifications with (2,1) and (0,3) imaginary self-dual flux. We also show that the most general GKP compactification leads to new classes of BPS and non-BPS multicenter solutions. We explore how these solutions fit into N = 2 truncations, and elucidate how supersymmetry becomes camouflaged. As a necessary tool in our exploration we show how the fields in the largest N = 2 truncation fit inside the six-torus compactification of eleven-dimensional supergravity.

Keywords

Flux compactifications Black Holes in String Theory D-branes M-Theory 
Download to read the full article text

References

  1. [1]
    M. Graña and J. Polchinski, Supersymmetric three form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [INSPIRE].ADSGoogle Scholar
  2. [2]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].MathSciNetADSGoogle Scholar
  3. [3]
    M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Supersymmetric backgrounds from generalized Calabi-Yau manifolds, JHEP 08 (2004) 046 [hep-th/0406137] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five-dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  5. [5]
    J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    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
  7. [7]
    K. Goldstein and S. Katmadas, Almost BPS black holes, JHEP 05 (2009) 058 [arXiv:0812.4183] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    A. Ceresole and G. Dall’Agata, Flow equations for non-BPS extremal black holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First order description of black holes in moduli space, JHEP 11 (2007) 032 [arXiv:0706.0712] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    G. Lopes Cardoso, A. Ceresole, G. Dall’Agata, J.M. Oberreuter and J. Perz, First-order flow equations for extremal black holes in very special geometry, JHEP 10 (2007) 063 [arXiv:0706.3373] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    B. Janssen, P. Smyth, T. Van Riet and B. Vercnocke, A first-order formalism for timelike and spacelike brane solutions, JHEP 04 (2008) 007 [arXiv:0712.2808] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    P. Galli and J. Perz, Non-supersymmetric extremal multicenter black holes with superpotentials, JHEP 02 (2010) 102 [arXiv:0909.5185] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    P. Galli, K. Goldstein, S. Katmadas and J. Perz, First-order flows and stabilisation equations for non-BPS extremal black holes, JHEP 06 (2011) 070 [arXiv:1012.4020] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].CrossRefGoogle Scholar
  18. [18]
    J. Held, D. Lüst, F. Marchesano and L. Martucci, DWSB in heterotic flux compactifications, JHEP 06 (2010) 090 [arXiv:1004.0867] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    I. Bena, H. Triendl and B. Vercnocke, Camouflaged supersymmetry, arXiv:1111.2601 [INSPIRE].
  20. [20]
    K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    K. Becker and M. Becker, Supersymmetry breaking, M-theory and fluxes, JHEP 07 (2001) 038 [hep-th/0107044] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N.P. Warner, Non-BPS black rings and black holes in taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    I. Bena, S. Giusto, C. Ruef and N.P. Warner, Multi-center non-BPS black holes: the solution, JHEP 11 (2009) 032 [arXiv:0908.2121] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    G. Bossard, Octonionic black holes, JHEP 05 (2012) 113 [arXiv:1203.0530] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M. Günaydin, G. Sierra and P. Townsend, The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M. Günaydin, G. Sierra and P. Townsend, Exceptional supergravity theories and the MAGIC square, Phys. Lett. B 133 (1983) 72 [INSPIRE].ADSGoogle Scholar
  27. [27]
    K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    D. Klemm and W. Sabra, General (Anti-)de Sitter black holes in five-dimensions, JHEP 02 (2001) 031 [hep-th/0011016] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    D. Klemm and W. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [31]
    I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity solutions from floating branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    I. Bena, C. Ruef and N.P. Warner, Imaginary soaring branes: a hidden feature of non-extremal solutions, JHEP 05 (2012) 143 [arXiv:1105.6255] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    H. Elvang, R. Emparan and P. Figueras, Non-supersymmetric black rings as thermally excited supertubes, JHEP 02 (2005) 031 [hep-th/0412130] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].MathSciNetADSGoogle Scholar
  35. [35]
    S.D. Mathur, The Fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  36. [36]
    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
  37. [37]
    S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [INSPIRE].
  38. [38]
    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
  39. [39]
    K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    B.D. Chowdhury and A. Virmani, Modave lectures on fuzzballs and emission from the D1-D5 system, arXiv:1001.1444 [INSPIRE].
  41. [41]
    G. Dall’Agata, S. Giusto and C. Ruef, U-duality and non-BPS solutions, JHEP 02 (2011) 074 [arXiv:1012.4803] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    G. Bossard and C. Ruef, Interacting non-BPS black holes, Gen. Rel. Grav. 44 (2012) 21 [arXiv:1106.5806] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  43. [43]
    I. Bena, M. Guica and W. Song, Un-twisting the NHEK with spectral flows, arXiv:1203.4227 [INSPIRE].
  44. [44]
    A. Sen and C. Vafa, Dual pairs of type-II string compactification, Nucl. Phys. B 455 (1995) 165 [hep-th/9508064] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  45. [45]
    M. Günaydin, Lectures on spectrum generating symmetries and U-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace, arXiv:0908.0374 [INSPIRE].
  46. [46]
    R. Gilmore, Lie groups, physics, and geometry: an introduction for physicists, engineers and chemists, Cambridge University Press, Cambridge U.K. (2008).MATHCrossRefGoogle Scholar
  47. [47]
    A. Tomasiello, Generalized structures of ten-dimensional supersymmetric solutions, JHEP 03 (2012) 073 [arXiv:1109.2603] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    S.S. Gubser, Supersymmetry and F-theory realization of the deformed conifold with three form flux, hep-th/0010010 [INSPIRE].
  49. [49]
    M. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [INSPIRE].ADSGoogle Scholar
  50. [50]
    S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477-478] [hep-th/9906070] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    J. Louis, P. Smyth and H. Triendl, Spontaneous N = 2 to N = 1 supersymmetry breaking in supergravity and type II string theory, JHEP 02 (2010) 103 [arXiv:0911.5077] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  52. [52]
    J. Louis, P. Smyth and H. Triendl, The N = 1 low-energy effective action of spontaneously broken N = 2 supergravities, JHEP 10 (2010) 017 [arXiv:1008.1214] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [INSPIRE].MathSciNetADSGoogle Scholar
  54. [54]
    I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].MathSciNetADSGoogle Scholar
  55. [55]
    B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.Institut de Physique Théorique, CEA Saclay,CNRS-URA 2306Gif sur YvetteFrance

Personalised recommendations