Supersymmetric AdS6 black holes from F(4) gauged supergravity

  • Minwoo Suh
Open Access
Regular Article - Theoretical Physics


In F (4) gauged supergravity in six dimensions, we study supersymmetric AdS6 black holes with various horizon geometries. We find a new \( Ad{S}_2 \times {\Sigma}_{\mathfrak{g}1}\times {\Sigma}_{\mathfrak{g}2} \) horizon solution with \( {\mathfrak{g}}_1>1 \) and \( {\mathfrak{g}}_2>1 \), and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically AdS6 boundary and the \( Ad{S}_2 \times {\Sigma}_{\mathfrak{g}1}\times {\Sigma}_{\mathfrak{g}2} \) horizon. We calculate the Bekenstein-Hawking entropy of the black hole and find a match with the recently calculated topologically twisted index of 5d USp(2N) gauge theory on \( {\Sigma}_{\mathfrak{g}1}\times {\Sigma}_{\mathfrak{g}2}\times {S}^1 \) in the large N limit. We also find black hole horizons of Kähler four-cycles in Calabi-Yau fourfolds and on Cayley four-cycles in Spin(7) manifolds.


AdS-CFT Correspondence Supergravity Models 


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.


  1. [1]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  2. [2]
    L.J. Romans, The F (4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
  3. [3]
    S. Ferrara, A. Kehagias, H. Partouche and A. Zaffaroni, AdS 6 interpretation of 5D superconformal field theories, Phys. Lett. B 431 (1998) 57 [hep-th/9804006] [INSPIRE].
  4. [4]
    N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
  5. [5]
    K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
  6. [6]
    M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    L.J. Romans, Massive N = 2a Supergravity in Ten-Dimensions, Phys. Lett. B 169 (1986) 374 [INSPIRE].
  8. [8]
    A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
  9. [9]
    J. Jeong, O. Kelekci and E. Ó Colgáin, An alternative IIB embedding of F (4) gauged supergravity, JHEP 05 (2013) 079 [arXiv:1302.2105] [INSPIRE].
  10. [10]
    J. Hong, J.T. Liu and D.R. Mayerson, Gauged Six-Dimensional Supergravity from Warped IIB Reductions, JHEP 09 (2018) 140 [arXiv:1808.04301] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    E. Malek, H. Samtleben and V. Vall Camell, Supersymmetric AdS 7 and AdS 6 vacua and their minimal consistent truncations from exceptional field theory, Phys. Lett. B 786 (2018) 171 [arXiv:1808.05597] [INSPIRE].
  12. [12]
    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].
  13. [13]
    C. Núñez, I.Y. 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].
  14. [14]
    M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
  15. [15]
    G. Dibitetto and N. Petri, Surface defects in the D4-D8 brane system, arXiv:1807.07768 [INSPIRE].
  16. [16]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
  17. [17]
    F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
  19. [19]
    S.M. Hosseini, I. Yaakov and A. Zaffaroni, Topologically twisted indices in five dimensions and holography, JHEP 11 (2018) 119 [arXiv:1808.06626] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  20. [20]
    P.M. Crichigno, D. Jain and B. Willett, 5d Partition Functions with A Twist, JHEP 11 (2018) 058 [arXiv:1808.06744] [INSPIRE].
  21. [21]
    J.P. Gauntlett and N. Kim, M five-branes wrapped on supersymmetric cycles. II, Phys. Rev. D 65 (2002) 086003 [hep-th/0109039] [INSPIRE].
  22. [22]
    F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  23. [23]
    J.P. Gauntlett, N. Kim and D. Waldram, M-fivebranes wrapped on supersymmetric cycles, Phys. Rev. D 63 (2001) 126001 [hep-th/0012195] [INSPIRE].
  24. [24]
    N. Bobev and P.M. Crichigno, Universal RG Flows Across Dimensions and Holography, JHEP 12 (2017) 065 [arXiv:1708.05052] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, JHEP 05 (2014) 032 [arXiv:1207.4359] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    J.P. Gauntlett, N.D. Lambert and P.C. West, Branes and calibrated geometries, Commun. Math. Phys. 202 (1999) 571 [hep-th/9803216] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    L. Andrianopoli, R. D’Auria and S. Vaula, Matter coupled F (4) gauged supergravity Lagrangian, JHEP 05 (2001) 065 [hep-th/0104155] [INSPIRE].
  28. [28]
    P. Karndumri, Twisted compactification of N = 2 5D SCFTs to three and two dimensions from F (4) gauged supergravity, JHEP 09 (2015) 034 [arXiv:1507.01515] [INSPIRE].
  29. [29]
    S.M. Hosseini, K. Hristov, A. Passias and A. Zaffaroni, 6D attractors and black hole microstates, arXiv:1809.10685 [INSPIRE].
  30. [30]
    M. Suh, Supersymmetric AdS 6 black holes from matter coupled F (4) gauged supergravity, arXiv:1810.00675 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsKyungpook National UniversityDaeguKorea

Personalised recommendations