Advertisement

Journal of High Energy Physics

, 2017:190 | Cite as

Holographic microstate counting for AdS4 black holes in massive IIA supergravity

  • Seyed Morteza Hosseini
  • Kiril Hristov
  • Achilleas Passias
Open Access
Regular Article - Theoretical Physics

Abstract

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS4 × S 6 from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional \( \mathcal{N}=2 \) Chern-Simons-matter gauge theories in the large N limit. The I-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic \( \mathcal{N}=2 \) gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on S 6. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.

Keywords

Black Holes in String Theory Gauge-gravity correspondence Supersymmetric Gauge Theory 

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]
    F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, arXiv:1605.06120 [INSPIRE].
  3. [3]
    A. Cabo-Bizet, Factorising the 3D topologically twisted index, JHEP 04 (2017) 115 [arXiv:1606.06341] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    C. Closset and H. Kim, Comments on twisted indices in 3D supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    C. Closset, H. Kim and B. Willett, Supersymmetric partition functions and the three-dimensional A-twist, JHEP 03 (2017) 074 [arXiv:1701.03171] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS 4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    A. Cabo-Bizet, V.I. Giraldo-Rivera and L.A. Pando Zayas, Microstate counting of AdS 4 hyperbolic black hole entropy via the topologically twisted index, JHEP 08 (2017) 023 [arXiv:1701.07893] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, Toward microstate counting beyond large-N in localization and the dual one-loop quantum supergravity, arXiv:1707.04197 [INSPIRE].
  11. [11]
    I. Jeon and S. Lal, Logarithmic corrections to entropy of magnetically charged AdS 4 black holes, Phys. Lett. B 774 (2017) 41 [arXiv:1707.04208] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    S.M. Hosseini and A. Zaffaroni, Large-N matrix models for 3d \( \mathcal{N}=2 \) theories: twisted index, free energy and black holes, JHEP 08 (2016) 064 [arXiv:1604.03122] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    S.M. Hosseini and N. Mekareeya, Large-N topologically twisted index: necklace quivers, dualities and Sasaki-Einstein spaces, JHEP 08 (2016) 089 [arXiv:1604.03397] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    O. Aharony, D. Jafferis, A. Tomasiello and A. Zaffaroni, Massive type IIA string theory cannot be strongly coupled, JHEP 11 (2010) 047 [arXiv:1007.2451] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    M. Petrini and A. Zaffaroni, N = 2 solutions of massive type IIA and their Chern-Simons duals, JHEP 09 (2009) 107 [arXiv:0904.4915] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [INSPIRE].CrossRefGoogle Scholar
  17. [17]
    A. Tomasiello and A. Zaffaroni, Parameter spaces of massive IIA solutions, JHEP 04 (2011) 067 [arXiv:1010.4648] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    A. Guarino, D.L. Jafferis and O. Varela, String theory origin of dyonic N = 8 supergravity and its Chern-Simons duals, Phys. Rev. Lett. 115 (2015) 091601 [arXiv:1504.08009] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    M. Fluder and J. Sparks, D2-brane Chern-Simons theories: F-maximization = a-maximization, JHEP 01 (2016) 048 [arXiv:1507.05817] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    Y. Pang and J. Rong, N = 3 solution in dyonic ISO(7) gauged maximal supergravity and its uplift to massive type IIA supergravity, Phys. Rev. D 92 (2015) 085037 [arXiv:1508.05376] [INSPIRE].ADSMathSciNetGoogle Scholar
  21. [21]
    Y. Pang and J. Rong, Evidence for the holographic dual of \( \mathcal{N}=3 \) solution in massive type IIA, Phys. Rev. D 93 (2016) 065038 [arXiv:1511.08223] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    A. Guarino, J. Tarrio and O. Varela, Romans-mass-driven flows on the D2-brane, JHEP 08 (2016) 168 [arXiv:1605.09254] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    A. Guarino and J. Tarrio, BPS black holes from massive IIA on S 6, arXiv:1703.10833 [INSPIRE].
  24. [24]
    A. Guarino, BPS black hole horizons from massive IIA, JHEP 08 (2017) 100 [arXiv:1706.01823] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    T.R. Araujo and H. Nastase, Observables in the Guarino-Jafferis-Varela/CS-SYM duality, JHEP 07 (2017) 020 [arXiv:1609.08008] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    T. Araujo, G. Itsios, H. Nastase and E. Ó. Colgáin, Penrose limits and spin chains in the GJV/CS-SYM duality, arXiv:1706.02711 [INSPIRE].
  27. [27]
    L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. 169B (1986) 374 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    A. Guarino and O. Varela, Consistent \( \mathcal{N}=8 \) truncation of massive IIA on S 6, JHEP 12 (2015) 020 [arXiv:1509.02526] [INSPIRE].ADSGoogle Scholar
  29. [29]
    D. Cassani, O. de Felice, M. Petrini, C. Strickland-Constable and D. Waldram, Exceptional generalised geometry for massive IIA and consistent reductions, JHEP 08 (2016) 074 [arXiv:1605.00563] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in N = 2 D = 4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    K. Hori, H. Kim and P. Yi, Witten index and wall crossing, JHEP 01 (2015) 124 [arXiv:1407.2567] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5D SCFT, JHEP 07 (2015) 063 [arXiv:1406.6793] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    C. Cordova and S.-H. Shao, An index formula for supersymmetric quantum mechanics, arXiv:1406.7853 [INSPIRE].
  35. [35]
    F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    S.M. Hosseini, A. Nedelin and A. Zaffaroni, The Cardy limit of the topologically twisted index and black strings in AdS 5, JHEP 04 (2017) 014 [arXiv:1611.09374] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    F. Azzurli, N. Bobev, P.M. Crichigno, V.S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS 4, arXiv:1707.04257 [INSPIRE].
  39. [39]
    F. Benini, H. Khachatryan and P. Milan, Black hole entropy in massive Type IIA, arXiv:1707.06886 [INSPIRE].
  40. [40]
    D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, JHEP 01 (2010) 015 [arXiv:0901.0969] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    N. Hama, K. Hosomichi and S. Lee, Notes on SUSY gauge theories on three-sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    P. Karndumri and E.O. Colgáin, 3D supergravity from wrapped D3-branes, JHEP 10 (2013) 094 [arXiv:1307.2086] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    D. Klemm, N. Petri and M. Rabbiosi, Black string first order flow in N = 2, D = 5 abelian gauged supergravity, JHEP 01 (2017) 106 [arXiv:1610.07367] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    A. Amariti and C. Toldo, Betti multiplets, flows across dimensions and c-extremization, JHEP 07 (2017) 040 [arXiv:1610.08858] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    A. Amariti, L. Cassia and S. Penati, Surveying 4d SCFTs twisted on Riemann surfaces, JHEP 06 (2017) 056 [arXiv:1703.08201] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    A. Amariti, L. Cassia and S. Penati, c-extremization from toric geometry, arXiv:1706.07752 [INSPIRE].
  50. [50]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  51. [51]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  53. [53]
    N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  54. [54]
    S. Katmadas, Static BPS black holes in U(1) gauged supergravity, JHEP 09 (2014) 027 [arXiv:1405.4901] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    N. Halmagyi, Static BPS black holes in AdS 4 with general dyonic charges, JHEP 03 (2015) 032 [arXiv:1408.2831] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    B. de Wit and M. van Zalk, Electric and magnetic charges in N = 2 conformal supergravity theories, JHEP 10 (2011) 050 [arXiv:1107.3305] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    K. Hristov, Lessons from the Vacuum Structure of 4d N = 2 Supergravity, Ph.D. Utrecht University, Uthrecht, Netherlands (2012), arXiv:1207.3830 [INSPIRE].
  59. [59]
    D. Klemm, N. Petri and M. Rabbiosi, Symplectically invariant flow equations for N = 2, D = 4 gauged supergravity with hypermultiplets, JHEP 04 (2016) 008 [arXiv:1602.01334] [INSPIRE].ADSMathSciNetGoogle Scholar
  60. [60]
    M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    K. Hristov, C. Toldo and S. Vandoren, On BPS bounds in D = 4 N = 2 gauged supergravity, JHEP 12 (2011) 014 [arXiv:1110.2688] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. [62]
    S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS 5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  64. [64]
    H. Samtleben, Lectures on gauged supergravity and flux compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Seyed Morteza Hosseini
    • 1
    • 2
  • Kiril Hristov
    • 3
  • Achilleas Passias
    • 4
  1. 1.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  2. 2.INFN — Sezione di Milano-BicoccaMilanoItaly
  3. 3.Institute for Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria
  4. 4.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

Personalised recommendations