Corrections to macroscopic supersymmetric black-hole entropy

  • Gabriel Lopes Cardoso
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 525)


We determine the corrections to the entropy of extremal black holes arising from terms quadratic in the Riemann tensor in N=2, D=4 supergravity theories. We follow Wald’s proposal to modify the Bekenstein-Hawking area law. The new entropy formula, whose value only depends on the electric/magnetic charges, is expressed in terms of a single holomorphic function and is consistent with electric-magnetic duality. For string effective field theories arising from Calabi-Yau compactifications, our result for the entropy of a certain class of extremal black-hole solutions fully agrees with the counting of microstates performed some time ago by Maldacena, Strominger, Witten and by Vafa.


Quantum Field Theory High Genus World Scientific High Energy Phys High Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J. M. Maldacena, A. Strominger and E. Witten, J. High Energy Phys. 12 (1997) 2, hep-th/9711053.CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    C. Vafa, Adv. Theor. Math. Phys. 2 (1998) 207, hep-th/9711067.zbMATHMathSciNetGoogle Scholar
  3. 3.
    S. Ferrara, R. Kallosh and A. Strominger, Phys. Rev. D52 (1995) 5412, hep-th/9508072ADSMathSciNetGoogle Scholar
  4. 3a.
    S. Ferrara and R. Kallosh, Phys. Rev. D54 (1996) 1514, hep-th/9602136; Phys. Rev. D54 (1996) 1525, hep-th/9603090.ADSMathSciNetGoogle Scholar
  5. 4.
    K. Behrndt, G. L. Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Nucl. Phys. B488 (1997) 236, hep-th/9610105.ADSGoogle Scholar
  6. 5.
    A. Strominger and C. Vafa, Phys. Lett. B379 (1996) 99, hep-th/9601029.ADSMathSciNetGoogle Scholar
  7. 6.
    K. Behrndt, G. L. Cardoso, B. de Wit, D. Lüst, T. Mohaupt and W. A. Sabra, Phys. Lett. B429 (1998) 289, hep-th/9801081.ADSGoogle Scholar
  8. 7.
    R. M. Wald, Phys. Rev. D48 (1993) 3427, gr-qc/9307038ADSMathSciNetGoogle Scholar
  9. 7a.
    T. Jacobson, G. Kang and R. C. Myers, Phys. Rev. D49 (1994) 6587, gr-qc/9312023ADSMathSciNetGoogle Scholar
  10. 7b.
    V. Iyer and R. M. Wald, Phys. Rev. D50 (1994) 846, gr-qc/9403028; T. Jacobson, G. Kang and R. C. Myers, Black-Hole Entropy in Higher Curvature Gravity, gr-qc/9502009.ADSMathSciNetGoogle Scholar
  11. 8.
    G. Gibbons, in Supersymmetry, Supergravity and Related Topics, eds. F. del Aguila, J. de Azcárraga and L. IbánẾz, World Scientific (1985) 147.Google Scholar
  12. 9.
    G. Moore, Attractors and Arithmetic, hep-th/9807056; Arithmetic and Attractors, hep-th/9807087.Google Scholar
  13. 10.
    B. de Wit, J. W. van Holten and A. Van Proeyen, Nucl. Phys. B167 (1980) 186, Nucl. Phys. B184 (1981) 77CrossRefADSGoogle Scholar
  14. 10a.
    B. de Wit and A. Van Proeyen, Nucl. Phys. B245 (1984) 89CrossRefADSGoogle Scholar
  15. 10b.
    B. de Wit, P. G. Lauwers and A. Van Proeyen, Nucl. Phys. B255 (1985) 569.ADSGoogle Scholar
  16. 11.
    E. Bergshoeff, M. de Roo and B. de Wit, Nucl. Phys. B182 (1981) 173.CrossRefADSGoogle Scholar
  17. 12.
    B. de Wit, Nucl. Phys. (Proc. Suppl.) B49 (1996) 191, hep-th/9602060; Fortsch. Phys. 44 (1996) 529, hep-th/9603191.ADSGoogle Scholar
  18. 13.
    G. L. Cardoso, B. de Wit and T. Mohaupt, to appear.Google Scholar
  19. 14.
    M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Nucl. Phys. B405 (1993) 279, hep-th/9302103; Comm. Math. Phys. 165 (1994) 311, hep-th/9309140.CrossRefADSMathSciNetGoogle Scholar
  20. 15.
    M. Mariño and G. Moore, Counting higher genus curves in a Calabi-Yau manifold, hep-th/9808131.Google Scholar
  21. 16.
    R. Gopakumar and C. Vafa, M-Theory and Topological Strings-I, hep-th/9809187.Google Scholar
  22. 17.
    M. Shmakova, Phys. Rev. D56 (1997) 540, hep-th/9612076.ADSMathSciNetGoogle Scholar
  23. 18.
    G. L. Cardoso, B. de Wit and T. Mohaupt, hep-th/9812082.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Gabriel Lopes Cardoso
    • 1
  1. 1.Institute for Theoretical PhysicsUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations