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Microstate counting of AdS 4 hyperbolic black hole entropy via the topologically twisted index

  • Alejandro Cabo-BizetEmail author
  • Victor I. Giraldo-Rivera
  • Leopoldo A. Pando Zayas
Open Access
Regular Article - Theoretical Physics

Abstract

We compute the topologically twisted index for general \( \mathcal{N}=2 \) supersymmetric field theories on \( {\mathrm{\mathbb{H}}}_2\times {S}^1 \). We also discuss asymptotically AdS 4 magnetically charged black holes with hyperbolic horizon, in four-dimensional \( \mathcal{N}=2 \) gauged supergravity. With certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find precise agreement between the black hole entropy and the topologically twisted index, for ABJ M theories.

Keywords

AdS-CFT Correspondence Black Holes in String Theory Chern-Simons Theories 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]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    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
  3. [3]
    F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    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
  5. [5]
    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
  6. [6]
    C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    A. Cabo-Bizet, Factorising the 3D Topologically Twisted Index, JHEP 04 (2017) 115 [arXiv:1606.06341] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    S.L. Cacciatori, D. Klemm, D.S. Mansi and E. Zorzan, All timelike supersymmetric solutions of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, JHEP 05 (2008) 097 [arXiv:0804.0009] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    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
  12. [12]
    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
  13. [13]
    N. Halmagyi, BPS Black Hole Horizons in N = 2 Gauged Supergravity, JHEP 02 (2014) 051 [arXiv:1308.1439] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A. Sen, Quantum Entropy Function from AdS 2 /CFT 1 Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP 06 (2011) 019 [arXiv:1012.0265] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    E.I. Buchbinder and A.A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling, Phys. Rev. D 89 (2014) 126008 [arXiv:1404.4952] [INSPIRE].ADSGoogle Scholar
  18. [18]
    J.R. David, E. Gava, R.K. Gupta and K. Narain, Localization on AdS 2 × S 1, JHEP 03 (2017) 050 [arXiv:1609.07443] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    B. Assel, D. Martelli, S. Murthy and D. Yokoyama, Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds, JHEP 03 (2017) 095 [arXiv:1609.08071] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    K. Hosomichi, A review on SUSY gauge theories on S 3, in New Dualities of Supersymmetric Gauge Theories, J. Teschner ed., pp. 307–338, (2016), [arXiv:1412.7128] [https://doi.org/10.1007/978-3-319-18769-3_10].
  22. [22]
    S. Cremonesi, An Introduction to Localisation and Supersymmetry in Curved Space, PoS(Modave 2013)002.
  23. [23]
    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
  24. [24]
    S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic Corrections to N = 4 and N = 8 Black Hole Entropy: A One Loop Test of Quantum Gravity, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    A. Faraggi, W. Mueck and L.A. Pando Zayas, One-loop Effective Action of the Holographic Antisymmetric Wilson Loop, Phys. Rev. D 85 (2012) 106015 [arXiv:1112.5028] [INSPIRE].ADSGoogle Scholar
  26. [26]
    A. Sen, Entropy Function and AdS 2 /CFT 1 Correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    G.V. Dunne, Aspects of Chern-Simons theory, in Topological Aspects of Low-dimensional Systems: Proceedings, Les Houches Summer School of Theoretical Physics, Session 69: Les Houches, France, July 7–31 1998, (1998), [hep-th/9902115] [INSPIRE].
  28. [28]
    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
  29. [29]
    R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    A. Comtet, On the Landau Levels on the Hyperbolic Plane, Annals Phys. 173 (1987) 185 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M. Antoine, A. Comtet and S. Ouvry, Scattering on an Hyperbolic Torus in a Constant Magnetic Field, J. Phys. A 23 (1990) 3699 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  32. [32]
    O. Lisovyy, Aharonov-Bohm effect on the Poincaré disk, J. Math. Phys. 48 (2007) 052112 [math-ph/0702066] [INSPIRE].
  33. [33]
    A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].ADSGoogle Scholar
  36. [36]
    J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
  38. [38]
    J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].ADSGoogle Scholar
  41. [41]
    R.K. Gupta and S. Murthy, All solutions of the localization equations for N = 2 quantum black hole entropy, JHEP 02 (2013) 141 [arXiv:1208.6221] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    P. Goddard, J. Nuyts and D.I. Olive, Gauge Theories and Magnetic Charge, Nucl. Phys. B 125 (1977) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    M. Nakahara, Geometry, topology and physics, Graduate student series in physics, Hilger, Bristol, U.S.A. (1990).Google Scholar
  44. [44]
    E. Witten, Supersymmetric index of three-dimensional gauge theory, hep-th/9903005 [INSPIRE].
  45. [45]
    X. Huang, S.-J. Rey and Y. Zhou, Three-dimensional SCFT on conic space as hologram of charged topological black hole, JHEP 03 (2014) 127 [arXiv:1401.5421] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    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
  47. [47]
    A.H. Chamseddine and W.A. Sabra, Magnetic strings in five-dimensional gauged supergravity theories, Phys. Lett. B 477 (2000) 329 [hep-th/9911195] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    D. Klemm and W.A. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].ADSMathSciNetGoogle Scholar
  49. [49]
    S. Banerjee, R.K. Gupta and A. Sen, Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    P. Benincasa and S. Nampuri, An SLE approach to four dimensional black hole microstate entropy, arXiv:1701.01864 [INSPIRE].
  51. [51]
    F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    S. Pasquetti, Factorisation of N = 2 Theories on the Squashed 3-Sphere, JHEP 04 (2012) 120 [arXiv:1111.6905] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    E. Gava, K.S. Narain, M.N. Muteeb and V.I. Giraldo-Rivera, N = 2 gauge theories on the hemisphere HS 4, Nucl. Phys. B 920 (2017) 256 [arXiv:1611.04804] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  54. [54]
    K. Hori and M. Romo, Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary, arXiv:1308.2438 [INSPIRE].
  55. [55]
    F. Nieri and S. Pasquetti, Factorisation and holomorphic blocks in 4d, JHEP 11 (2015) 155 [arXiv:1507.00261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    M. Honda and Y. Yoshida, Supersymmetric index on T 2 × S 2 and elliptic genus, arXiv:1504.04355 [INSPIRE].
  57. [57]
    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

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Alejandro Cabo-Bizet
    • 1
    Email author
  • Victor I. Giraldo-Rivera
    • 2
    • 3
  • Leopoldo A. Pando Zayas
    • 4
  1. 1.Instituto de Astronomía y Física del Espacio (CONICET-UBA)Buenos AiresArgentina
  2. 2.International Centre for Theoretical Sciences (ICTS-TIFR)BengaluruIndia
  3. 3.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  4. 4.Michigan Center for Theoretical Physics Randall Laboratory of PhysicsThe University of MichiganAnn ArborU.S.A.

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