Logarithmic corrections to black hole entropy: the non-BPS branch

  • Alejandra Castro
  • Victor Godet
  • Finn Larsen
  • Yangwenxiao Zeng
Open Access
Regular Article - Theoretical Physics
  • 16 Downloads

Abstract

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D \( \mathcal{N}\ge 2 \) supergravity theories. This branch corresponds to finite temperature black holes whose extremal limit does not preserve supersymmetry, such as the D0 − D6 system in string theory. Starting from a black hole in minimal Kaluza-Klein theory, we discuss in detail its embedding into \( \mathcal{N}=8 \), 6, 4, 2 supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the c-anomaly vanishes only when \( \mathcal{N}\ge 6 \), in contrast to the BPS branch where c vanishes for all \( \mathcal{N}\ge 2 \). We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

Keywords

Black Holes in String Theory Extended Supersymmetry 

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. 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].ADSCrossRefMATHGoogle Scholar
  2. [2]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    A. Sen, Logarithmic corrections to N = 2 black hole entropy: an infrared window into the microstates, Gen. Rel. Grav. 44 (2012) 1207 [arXiv:1108.3842] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    A. Sen, Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions, Gen. Rel. Grav. 44 (2012) 1947 [arXiv:1109.3706] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Chowdhury, R.K. Gupta, S. Lal, M. Shyani and S. Thakur, Logarithmic corrections to twisted indices from the quantum entropy function, JHEP 11 (2014) 002 [arXiv:1404.6363] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    R.K. Gupta, S. Lal and S. Thakur, Logarithmic corrections to extremal black hole entropy in N = 2, 4 and 8 supergravity, JHEP 11 (2014) 072 [arXiv:1402.2441] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    C. Keeler, F. Larsen and P. Lisbao, Logarithmic corrections to N ≥ 2 black hole entropy, Phys. Rev. D 90 (2014) 043011 [arXiv:1404.1379] [INSPIRE].ADSGoogle Scholar
  8. [8]
    C. Keeler and G.S. Ng, Partition functions in even dimensional AdS via quasinormal mode methods, JHEP 06 (2014) 099 [arXiv:1401.7016] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    F. Larsen and P. Lisbao, Quantum corrections to supergravity on AdS 2 × S 2, Phys. Rev. D 91 (2015) 084056 [arXiv:1411.7423] [INSPIRE].ADSGoogle Scholar
  10. [10]
    I. Mandal and A. Sen, Black hole microstate counting and its macroscopic counterpart, Nucl. Phys. Proc. Suppl. 216 (2011) 147 [Class. Quant. Grav. 27 (2010) 214003] [arXiv:1008.3801] [INSPIRE].
  11. [11]
    A. Sen, Microscopic and macroscopic entropy of extremal black holes in string theory, Gen. Rel. Grav. 46 (2014) 1711 [arXiv:1402.0109] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A one-loop test of quantum supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    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
  14. [14]
    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, JHEP 01 (2018) 026 [arXiv:1707.04197] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, A one-loop test of quantum black holes in anti de Sitter space, arXiv:1711.01076 [INSPIRE].
  16. [16]
    A. Sen, Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions, JHEP 04 (2013) 156 [arXiv:1205.0971] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    A.M. Charles and F. Larsen, Universal corrections to non-extremal black hole entropy in N ≥ 2 supergravity, JHEP 06 (2015) 200 [arXiv:1505.01156] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    A. Pathak, A.P. Porfyriadis, A. Strominger and O. Varela, Logarithmic corrections to black hole entropy from Kerr/CFT, JHEP 04 (2017) 090 [arXiv:1612.04833] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    S.W. Hawking, Zeta function regularization of path integrals in curved space-time, Commun. Math. Phys. 55 (1977) 133 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, Cambridge U.K., (1984) [INSPIRE].
  21. [21]
    D.V. Vassilevich, Heat kernel expansion: user’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    A.M. Charles, F. Larsen and D.R. Mayerson, Non-renormalization for non-supersymmetric black holes, JHEP 08 (2017) 048 [arXiv:1702.08458] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    G.T. Horowitz and T. Wiseman, General black holes in Kaluza-Klein theory, arXiv:1107.5563 [INSPIRE].
  26. [26]
    E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  28. [28]
    F. Larsen and E.J. Martinec, Currents and moduli in the (4, 0) theory, JHEP 11 (1999) 002 [hep-th/9909088] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    M. Cvetič and F. Larsen, Black holes with intrinsic spin, JHEP 11 (2014) 033 [arXiv:1406.4536] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Extremal black holes in supergravity, Lect. Notes Phys. 737 (2008) 661 [hep-th/0611345] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge Univ. Press, Cambridge U.K., (2012) [INSPIRE].
  32. [32]
    P.K. Tripathy and S.P. Trivedi, Non-supersymmetric attractors in string theory, JHEP 03 (2006) 022 [hep-th/0511117] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    S. Bellucci, S. Ferrara, M. Günaydin and A. Marrani, Charge orbits of symmetric special geometries and attractors, Int. J. Mod. Phys. A 21 (2006) 5043 [hep-th/0606209] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    D. Brizuela, J.M. Martin-Garcia and G.A. Mena Marugan, xPert: computer algebra for metric perturbation theory, Gen. Rel. Grav. 41 (2009) 2415 [arXiv:0807.0824] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    F. Larsen, Kaluza-Klein black holes in string theory, in Proceedings, 7th International Symposium on Particles, Strings and Cosmology (PASCOS 99), Lake Tahoe CA U.S.A., 10–16 December 1999, World Scientific, Singapore, (2000), pg. 57 [hep-th/0002166] [INSPIRE].
  36. [36]
    R. Emparan and G.T. Horowitz, Microstates of a neutral black hole in M-theory, Phys. Rev. Lett. 97 (2006) 141601 [hep-th/0607023] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    E.G. Gimon, F. Larsen and J. Simon, Black holes in supergravity: the non-BPS branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    E.G. Gimon, F. Larsen and J. Simon, Constituent model of extremal non-BPS black holes, JHEP 07 (2009) 052 [arXiv:0903.0719] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    A. Belin, A. Castro, J. Gomes and C.A. Keller, Siegel modular forms and black hole entropy, JHEP 04 (2017) 057 [arXiv:1611.04588] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    D. Anninos, T. Anous and R.T. D’Agnolo, Marginal deformations & rotating horizons, JHEP 12 (2017) 095 [arXiv:1707.03380] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  42. [42]
    A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS 2 /nCFT 1 correspondence, work in progress.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Alejandra Castro
    • 1
  • Victor Godet
    • 1
  • Finn Larsen
    • 2
  • Yangwenxiao Zeng
    • 2
  1. 1.Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Physics and Leinweber Center for Theoretical PhysicsUniversity of MichiganAnn ArborU.S.A.

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