Quantum black holes in Type-IIA String Theory

Article

Abstract

We study black hole solutions of Type-IIA Calabi-Yau compactifications in the presence of quantum perturbative corrections. We define a class of black holes that only exist in the presence of quantum corrections and that, consequently, can be considered as purely quantum black holes. The regularity conditions of the solutions impose the topological constraint h 1,1 > h 2,1 on the Calabi-Yau manifold, defining a class of admissible compactifications, which we prove to be non-empty for h 1,1 = 3 by explicitly constructing the corresponding Calabi-Yau manifolds, new in the literature.

Keywords

Black Holes in String Theory Differential and Algebraic Geometry 

References

  1. [1]
    S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    W. Chemissany et al., Black holes in supergravity and integrability, JHEP 09 (2010) 080 [arXiv:1007.3209] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    W. Chemissany, J. Rosseel and T. Van Riet, Black holes as generalised Toda molecules, Nucl. Phys. B 843 (2011) 413 [arXiv:1009.1487] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T. Mohaupt and O. Vaughan, Non-extremal Black Holes, Harmonic Functions and Attractor Equations, Class. Quant. Grav. 27 (2010) 235008 [arXiv:1006.3439] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    T. Mohaupt and O. Vaughan, The Hesse potential, the c-map and black hole solutions, JHEP 07 (2012) 163 [arXiv:1112.2876] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, arXiv:1207.2679 [INSPIRE].
  7. [7]
    A. de Antonio Martin, T. Ortín and C. Shahbazi, The FGK formalism for black p-branes in d dimensions, JHEP 05 (2012) 045 [arXiv:1203.0260] [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    K. Behrndt and I. Gaida, Subleading contributions from instanton corrections in N = 2 supersymmetric black hole entropy, Phys. Lett. B 401 (1997) 263 [hep-th/9702168] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    K. Behrndt, G. Lopes Cardoso and I. Gaida, Quantum N = 2 supersymmetric black holes in the S-T model, Nucl. Phys. B 506 (1997) 267 [hep-th/9704095] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and nonholomorphic corrections for supersymmetric black holes, Nucl. Phys. B 567 (2000) 87 [hep-th/9906094] [INSPIRE].CrossRefGoogle Scholar
  11. [11]
    T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  12. [12]
    S. Bellucci, A. Marrani and R. Roychowdhury, On Quantum Special Kähler Geometry, Int. J. Mod. Phys. A 25 (2010) 1891 [arXiv:0910.4249] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    S. Bellucci, S. Ferrara, A. Marrani and A. Shcherbakov, Splitting of attractors in 1-modulus quantum corrected special geometry, JHEP 02 (2008) 088 [arXiv:0710.3559] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    S. Bellucci, S. Ferrara, A. Marrani and A. Shcherbakov, Quantum lift of non-bps flat directions, Phys. Lett. B 672 (2009) 77 [arXiv:0811.3494] [INSPIRE].MathSciNetADSGoogle Scholar
  15. [15]
    P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    P. Candelas, X.C. De la Ossa, P.S. Green and L. Parkes, An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds, Phys. Lett. B 258 (1991) 118 [INSPIRE].ADSGoogle Scholar
  18. [18]
    B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].ADSMATHCrossRefGoogle Scholar
  19. [19]
    B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    P. Galli, T. Ortín, J. Perz and C.S. Shahbazi, Non-extremal black holes of N = 2, D = 4 supergravity, JHEP 07 (2011) 041 [arXiv:1105.3311] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    P. Meessen, T. Ortín, J. Perz and C. Shahbazi, H-FGK formalism for black-hole solutions of N = 2, D = 4 and D = 5 supergravity, Phys. Lett. B 709 (2012) 260 [arXiv:1112.3332] [INSPIRE].ADSGoogle Scholar
  22. [22]
    P. Meessen, T. Ortín, J. Perz and C. Shahbazi, Black holes and black strings of N = 2, D = 5 supergravity in the H-FGK formalism, JHEP 09 (2012) 001 [arXiv:1204.0507] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    P. Candelas, A. Dale, C. Lütken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds, Nucl. Phys. B 298 (1988) 493 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [INSPIRE].MathSciNetMATHGoogle Scholar
  25. [25]
    M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240] [INSPIRE].MathSciNetGoogle Scholar
  26. [26]
    P. Candelas and R. Davies, New Calabi-Yau Manifolds with Small Hodge Numbers, Fortsch. Phys. 58 (2010) 383 [arXiv:0809.4681] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  27. [27]
    V. Braun, On free quotients of complete intersection Calabi-Yau manifolds, JHEP 04 (2011) 005 [arXiv:1003.3235] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    R. Davies, The Expanding Zoo of Calabi-Yau Threefolds, Adv. High Energy Phys. 2011 (2011) 901898 [arXiv:1103.3156] [INSPIRE].Google Scholar
  29. [29]
    R. Davies, Quotients of the conifold in compact Calabi-Yau threefolds and new topological transitions, Adv. Theor. Math. Phys. 14 (2010) 965 [arXiv:0911.0708] [INSPIRE].MathSciNetMATHGoogle Scholar
  30. [30]
    R. Davies, Hyperconifold transitions, mirror symmetry and string theory, Nucl. Phys. B 850 (2011) 214 [arXiv:1102.1428] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    P. Candelas and A. Constantin, Completing the web of Z 3-quotients of complete intersection Calabi-Yau manifolds, Fortsch. Phys. 60 (2012) 345 [arXiv:1010.1878] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  32. [32]
    V. Braun, P. Candelas and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, Fortsch. Phys. 58 (2010) 467 [arXiv:0910.5464] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  33. [33]
    P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    A. Strominger and E. Witten, New manifolds for superstring compactification, Commun. Math. Phys. 101 (1985) 341 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    P. Candelas, E. Derrick and L. Parkes, Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B 407 (1993) 115 [hep-th/9304045] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Instituto de Física Teórica UAM/CSICMadridSpain
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.
  3. 3.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordU.S.A.

Personalised recommendations