Advertisement

AdS black holes from duality in gauged supergravity

  • Nick HalmagyiEmail author
  • Thomas Vanel
Open Access
Article

Abstract

We study and utilize duality transformations in a particular STU-model of four dimensional gauged supergravity. This model is a truncation of the de Wit-Nicolai \( \mathcal{N} \) =8 theory and as such has a lift to eleven-dimensional supergravity on the seven-sphere. Our duality group is U(1)3 and while it can be applied to any solution of this theory, we consider known asymptotically AdS4, supersymmetric black holes and focus on duality transformations which preserve supersymmetry. For static black holes we generalize the supersymmetric solutions of Cacciatori and Klemm from three magnetic charges to include two additional electric charges and argue that this is co-dimension one in the full space of supersymmetric static black holes in the STU-model. These new static black holes have nontrivial profiles for axions. For rotating black holes, we generalize the known two-parameter supersymmetric solution to include an additional parameter. When lifted to M-theory, these black holes correspond to the near horizon geometry of a stack of BPS rotating M2-branes, spinning on an S 7 which is fibered non-trivially over a Riemann surface.

Keywords

Gauge-gravity correspondence Black Holes in String Theory AdS-CFT Correspondence Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    D. Klemm, Rotating BPS black holes in matter-coupled AdS 4 supergravity, JHEP 07 (2011) 019 [arXiv:1103.4699] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    C. Núñez, I. Park, M. Schvellinger and T.A. Tran, Supergravity duals of gauge theories from F(4) gauged supergravity in six-dimensions, JHEP 04 (2001) 025 [hep-th/0103080] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    S. Cucu, H. Lü and J.F. Vazquez-Poritz, A supersymmetric and smooth compactification of M-theory to AdS 5, Phys. Lett. B 568 (2003) 261 [hep-th/0303211] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Cucu, H. Lü and J.F. Vazquez-Poritz, Interpolating from AdS(D − 2) × S 2 to AdS(D), Nucl. Phys. B 677 (2004) 181 [hep-th/0304022] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
  11. [11]
    F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J.P. Gauntlett, Branes, calibrations and supergravity, hep-th/0305074 [INSPIRE].
  13. [13]
    M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    D. Klemm and W. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    R.P. Geroch, A method for generating solutions of Einsteins equations, J. Math. Phys. 12 (1971) 918 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. [16]
    B. de Wit and H. Nicolai, N = 8 supergravity with local SO(8) × SU(8) Invariance, Phys. Lett. B 108 (1982) 285 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    M. Cvetič, M. Duff, P. Hoxha, J.T. Liu, H. Lü et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    H. Nicolai and K. Pilch, Consistent truncation of D = 11 supergravity on AdS 4 × S 7, JHEP 03 (2012) 099 [arXiv:1112.6131] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    B. de Wit and H. Nicolai, The consistency of the S 7 truncation in D = 11 supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  23. [23]
    B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    R. Corrado, M. Günaydin, N.P. Warner and M. Zagermann, Orbifolds and flows from gauged supergravity, Phys. Rev. D 65 (2002) 125024 [hep-th/0203057] [INSPIRE].ADSGoogle Scholar
  25. [25]
    A. Gnecchi and N. Halmagyi, Supersymmetric black holes in AdS 4 from very special geometry, arXiv:1312.2766 [INSPIRE].
  26. [26]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    N. Halmagyi, BPS black hole horizons in N = 2 gauged supergravity, JHEP 02 (2014) 051 [arXiv:1308.1439] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    A. Gnecchi, K. Hristov, D. Klemm, C. Toldo and O. Vaughan, Rotating black holes in 4D gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  29. [29]
    N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  30. [30]
    D.D.K. Chow and G. Compére, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].ADSGoogle Scholar
  31. [31]
    V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    M. Cvetič, G. Gibbons, H. Lü and C. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
  33. [33]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, JHEP 01 (2013) 053 [arXiv:1207.2679] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    A. Gnecchi and C. Toldo, On the non-BPS first order flow in N = 2 U(1)-gauged supergravity, JHEP 03 (2013) 088 [arXiv:1211.1966] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  35. [35]
    K. Hristov, C. Toldo and S. Vandoren, Phase transitions of magnetic AdS 4 black holes with scalar hair, Phys. Rev. D 88 (2013) 026019 [arXiv:1304.5187] [INSPIRE].ADSGoogle Scholar
  36. [36]
    A. Anabalón and D. Astefanesei, On attractor mechanism of AdS 4 black holes, Phys. Lett. B 727 (2013) 568 [arXiv:1309.5863] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    A. Anabalon and D. Astefanesei, Black holes in ω-defomed gauged N = 8 supergravity, arXiv:1311.7459 [INSPIRE].
  38. [38]
    H. Lü, Y. Pang and C. Pope, AdS dyonic black hole and its thermodynamics, JHEP 11 (2013) 033 [arXiv:1307.6243] [INSPIRE].CrossRefGoogle Scholar
  39. [39]
    O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  40. [40]
    S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    O. Aharony, B. Kol and S. Yankielowicz, On exactly marginal deformations of N = 4 SYM and type IIB supergravity on AdS 5 × S 5, JHEP 06 (2002) 039 [hep-th/0205090] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  42. [42]
    R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N =1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95[hep-th/9503121] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  43. [43]
    M. Berkooz and B. Pioline, 5D black holes and non-linear σ-models, JHEP 05 (2008) 045 [arXiv:0802.1659] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  44. [44]
    L. Andrianopoli et al., General matter coupled N = 2 supergravity, Nucl. Phys. B 476 (1996) 397 [hep-th/9603004] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  45. [45]
    B. de Wit and A. Van Proeyen, Hidden symmetries, special geometry and quaternionic manifolds, Int. J. Mod. Phys. D 3 (1994) 31 [hep-th/9310067] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité Pierre et Marie Curie, CNRS UMR 7589Paris Cedex 05France

Personalised recommendations