Journal of High Energy Physics

, 2014:51 | Cite as

BPS black hole horizons in N=2 gauged supergravity

  • Nick HalmagyiEmail author
Open Access


We study static BPS black hole horizons in four dimensional \( \mathcal{N} \) = 2 gauged supergravity coupled to n v -vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form AdS 2 × Σ g . In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. When the special Kähler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. For more general models our solution is implicit up to a set of holomorphic quadratic equations. For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin.


Black Holes in String Theory AdS-CFT Correspondence Black Holes Supergravity Models 


Open Access

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  1. [1]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    M.M. Caldarelli and D. Klemm, Supersymmetry of anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, D = 4 black hole attractors in N = 2 supergravity with Fayet-Iliopoulos terms, Phys. Rev. D 77 (2008) 085027 [arXiv:0802.0141].ADSMathSciNetGoogle Scholar
  5. [5]
    T. Kimura, Non-supersymmetric extremal RN-AdS black holes in N = 2 gauged supergravity, JHEP 09 (2010) 061 [arXiv:1005.4607].ADSCrossRefGoogle Scholar
  6. [6]
    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].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    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].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    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].ADSGoogle Scholar
  10. [10]
    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].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    S. Barisch, G.L. Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and electric AdS solutions in string- and M-theory, Class. and Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    J. Maldacena and C. Nuñez, Supergravity Description of Field Theories on Curved Manifolds and a no GO Theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018].ADSCrossRefGoogle Scholar
  15. [15]
    J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250].ADSMathSciNetGoogle Scholar
  16. [16]
    S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072].ADSMathSciNetGoogle Scholar
  17. [17]
    K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169].ADSCrossRefGoogle Scholar
  18. [18]
    B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289].CrossRefGoogle Scholar
  19. [19]
    B. de Wit and M. van Zalk, Electric and magnetic charges in N = 2 conformal supergravity theories, JHEP 10 (2011) 050 [arXiv:1107.3305].CrossRefGoogle Scholar
  20. [20]
    L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara and P. Fré, General matter coupled N = 2 supergravity, Nucl. Phys. B 476 (1996) 397 [hep-th/9603004].ADSCrossRefGoogle Scholar
  21. [21]
    M. Shmakova, Calabi-Yau Black Holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076].ADSMathSciNetGoogle Scholar
  22. [22]
    S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090].ADSMathSciNetGoogle Scholar
  23. [23]
    S. Ferrara and M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory, Int. J. Mod. Phys. A 13 (1998) 2075 [hep-th/9708025] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    B. Pioline, Lectures on black holes, topological strings and quantum attractors, Class. Quant. Grav. 23 (2006) S981 [hep-th/0607227] [INSPIRE].ADSCrossRefMathSciNetGoogle 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]
    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
  27. [27]
    N. Halmagyi, work in progress.Google Scholar
  28. [28]
    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
  29. [29]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza-Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [INSPIRE].ADSCrossRefMathSciNetGoogle 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

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