Journal of High Energy Physics

, 2013:112 | Cite as

Charged dilatonic ads black holes and magnetic AdS D−2 × R 2 vacua



We consider D-dimensional Einstein gravity coupled to two U(1) fields and a dilaton with a scalar potential. We derive the condition that the analytical AdS black holes with two independent charges can be constructed. Turning off the cosmological constant, the extremal Reissner-Nordstrøm black hole emerges as the harmonic superposition of the two U(1) building blocks. With the non-vanishing cosmological constant, our extremal solutions contain the near-horizon geometry of AdS2 ×R D−2 with or without a hyperscaling. We also obtain the magnetic \( \mathrm{Ad}{{\mathrm{S}}_{D-2 }}\times {{\mathcal{Y}}^2} \) vacua where \( {{\mathcal{Y}}^2} \) can be R 2, S 2 or hyperbolic 2-space. These vacua arise as the fix points of some super potentials and recover the known supersymmetric vacua when the theory can be embedded in gauged supergravities. The AdSD−2 × R 2 vacua are of particular interest since they are dual to some quantum field theories at the lowest Landau level. By studying the embedding of some of these solutions in the string and M-theory, we find that the M2/M5-system with the equal M2 and M5 charges can intersect with another such M2/M5 on to a dyonic black hole. Analogous intersection rule applies also to the D1/D5-system. The intersections are non-supersymmetric but in the manner of harmonic superpositions.


Black Holes Classical Theories of Gravity Supergravity Models 


  1. [1]
    K. Behrndt, M. Cvetič and W.A. Sabra, Nonextreme black holes of five-dimensional N = 2 AdS supergravity, Nucl. Phys. B 553 (1999) 317 [hep-th/9810227] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M.J. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M. Cvetič, H. Lü and C. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  5. [5]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, JHEP 01 (2013) 053 [arXiv:1207.2679] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry II, Class. Quant. Grav. 30 (2013) 065003 [arXiv:1211.1618] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    Z.-W. Chong, M. Cvetič, H. Lü and C. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S.-Q. Wu, General nonextremal rotating charged AdS black holes in five-dimensional U(1)3 gauged supergravity: a simple construction method, Phys. Lett. B 707 (2012) 286 [arXiv:1108.4159] [INSPIRE].ADSGoogle Scholar
  9. [9]
    Z.-W. Chong, M. Cvetič, H. Lü and C. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    D.D. Chow, Equal charge black holes and seven dimensional gauged supergravity, Class. Quant. Grav. 25 (2008) 175010 [arXiv:0711.1975] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    D.D. Chow, Charged rotating black holes in six-dimensional gauged supergravity, Class. Quant. Grav. 27 (2010) 065004 [arXiv:0808.2728] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J. Rahmfeld, Extremal black holes as bound states, Phys. Lett. B 372 (1996) 198 [hep-th/9512089] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    A.A. Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B 475 (1996) 149 [hep-th/9604035] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    H. Lü and Z.-L. Wang, Pseudo-Killing spinors, pseudo-supersymmetric p-branes, bubbling and less-bubbling AdS spaces, JHEP 06 (2011) 113 [arXiv:1103.0563] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    H. Lü, C. Pope and Z.-L. Wang, Pseudo-supersymmetry, consistent sphere reduction and Killing spinors for the bosonic string, Phys. Lett. B 702 (2011) 442 [arXiv:1105.6114] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    H. Lü and Z.-L. Wang, Killing Spinors for the Bosonic String, Europhys. Lett. 97 (2012) 50010 [arXiv:1106.1664] [INSPIRE].CrossRefGoogle Scholar
  17. [17]
    H. Liu, H. Lü and Z.-L. Wang, Killing spinors for the bosonic string and the Kaluza-Klein theory with scalar potentials, Eur. Phys. J. C 72 (2012) 1853 [arXiv:1106.4566] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    H. Lü, C.N. Pope and Z.-L. Wang, Pseudo-supergravity extension of the bosonic string, Nucl. Phys. B 854 (2012) 293 [arXiv:1106.5794] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    H.-S. Liu, H. Lü, Z.-L. Wang, H. Lü and Z.-L. Wang, Gauged Kaluza-Klein AdS pseudo-supergravity, Phys. Lett. B 703 (2011) 524 [arXiv:1107.2659] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    D.D. Chow, Single-rotation two-charge black holes in gauged supergravity, arXiv:1108.5139 [INSPIRE].
  21. [21]
    S.-Q. Wu, General rotating charged Kaluza-Klein AdS black holes in higher dimensions, Phys. Rev. D 83 (2011) 121502 [arXiv:1108.4157] [INSPIRE].ADSGoogle Scholar
  22. [22]
    K.C.K. Chan, J.H. Horne and R.B. Mann, Charged dilaton black holes with unusual asymptotics, Nucl. Phys. B 447 (1995) 441 [gr-qc/9502042] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    H. Lü, C.N. Pope, E. Sezgin and K. Stelle, Stainless super p-branes, Nucl. Phys. B 456 (1995) 669 [hep-th/9508042] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    T. Ortin, Gravity and strings, Cambridge University Press, Cambridge U.K. (2004).CrossRefMATHGoogle Scholar
  25. [25]
    A. Almuhairi and J. Polchinski, Magnetic AdS ×R 2 : supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
  26. [26]
    H. Lü, C. Pope and K. Xu, Liouville and Toda solutions of M-theory, Mod. Phys. Lett. A 11 (1996) 1785 [hep-th/9604058] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    H. Lü and W. Yang, SL(n, R)-Toda black holes, arXiv:1307.2305 [INSPIRE].
  28. [28]
    R.L. Arnowitt, S. Deser and C.W. Misner, Dynamical structure andl definition of energy in general relativity, Phys. Rev. 116 (1959) 1322 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  29. [29]
    M. Cvetič and D. Youm, Entropy of nonextreme charged rotating black holes in string theory, Phys. Rev. D 54 (1996) 2612 [hep-th/9603147] [INSPIRE].ADSGoogle Scholar
  30. [30]
    F. Larsen, A String model of black hole microstates, Phys. Rev. D 56 (1997) 1005 [hep-th/9702153] [INSPIRE].ADSGoogle Scholar
  31. [31]
    M. Cvetič and F. Larsen, General rotating black holes in string theory: grey body factors and event horizons, Phys. Rev. D 56 (1997) 4994 [hep-th/9705192] [INSPIRE].ADSGoogle Scholar
  32. [32]
    M. Cvetič and F. Larsen, Grey body factors for rotating black holes in four-dimensions, Nucl. Phys. B 506 (1997) 107 [hep-th/9706071] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    Y.-X. Chen, H. Lü and K.-N. Shao, Linearized modes in extended and critical gravities, Class. Quant. Grav. 29 (2012) 085017 [arXiv:1108.5184] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    H. Lü and K.-N. Shao, Solutions of free higher spins in AdS, Phys. Lett. B 706 (2011) 106 [arXiv:1110.1138] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Townsend and P. van Nieuwenhuizen, Gauged seven-dimensional supergravity, Phys. Lett. B 125 (1983) 41 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    L. Romans, The F (4) gauged supergravity in six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    H. Lü, C. Pope, E. Sezgin and K. Stelle, Dilatonic p-brane solitons, Phys. Lett. B 371 (1996) 46 [hep-th/9511203] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    M. Bremer, M. Duff, H. Lü, C. Pope and K. Stelle, Instanton cosmology and domain walls from M-theory and string theory, Nucl. Phys. B 543 (1999) 321 [hep-th/9807051] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    H. Liu, H. Lü and Z.-L. Wang, f (R) theories of supergravities and pseudo-supergravities, JHEP 04 (2012) 072 [arXiv:1201.2417] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    W. Chen, H. Lü and C. Pope, Mass of rotating black holes in gauged supergravities, Phys. Rev. D 73 (2006) 104036 [hep-th/0510081] [INSPIRE].ADSGoogle Scholar
  41. [41]
    A. Ashtekar and A. Magnon, Asymptotically Anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  43. [43]
    L. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  44. [44]
    N. Alonso-Alberca, P. Meessen and T. Ortín, Supersymmetry of topological Kerr-Newman-Taub-NUT-AdS space-times, Class. Quant. Grav. 17 (2000) 2783 [hep-th/0003071] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  45. [45]
    H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    Z.-W. Chong, H. Lü and C. Pope, BPS geometries and AdS bubbles, Phys. Lett. B 614 (2005) 96 [hep-th/0412221] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    C. Toldo and S. Vandoren, Static nonextremal AdS 4 black hole solutions, JHEP 09 (2012) 048 [arXiv:1207.3014] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  50. [50]
    M. Cvetič, G. Gibbons and C. Pope, Universal area product formulae for rotating and charged black holes in four and higher dimensions, Phys. Rev. Lett. 106 (2011) 121301 [arXiv:1011.0008] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    S.S. Gubser and J. Ren, Analytic fermionic Greens functions from holography, Phys. Rev. D 86 (2012) 046004 [arXiv:1204.6315] [INSPIRE].ADSGoogle Scholar
  52. [52]
    J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    A. Das, M. Fischler and M. Roček, Super-Higgs effect in a new class of scalar models and a model of super QED, Phys. Rev. D 16 (1977) 3427 [INSPIRE].ADSGoogle Scholar
  54. [54]
    G. Gibbons and D. Wiltshire, Black holes in Kaluza-Klein theory, Annals Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    M. Cvetič, H. Lü and C. Pope, Four-dimensional N = 4, SO(4) gauged supergravity from D=11,Nucl. Phys. B 574 (2000) 761 [hep-th/9910252] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    S. Cucu, H. Lü and J.F. Vázquez-Poritz, A supersymmetric and smooth compactification of M-theory to AdS 5, Phys. Lett. B 568 (2003) 261 [hep-th/0303211] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    S. Cucu, H. Lü and J.F. Vázquez-Poritz, Interpolating from AdS D−2 × S 2 to AdS D , Nucl. Phys. B 677 (2004) 181 [hep-th/0304022] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    A. Almuhairi, AdS 3 and AdS 2 magnetic brane solutions, arXiv:1011.1266 [INSPIRE].
  59. [59]
    M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  60. [60]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    S. Cacciatori, D. Klemm and D. Zanon, W algebras, conformal mechanics and black holes, Class. Quant. Grav. 17 (2000) 1731 [hep-th/9910065] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  62. [62]
    D. Klemm and W. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Normal UniversityBeijingChina

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