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Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime

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Abstract

We study Einstein-Maxwell-dilaton gravity models in four-dimensional antide Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a “Drude peak”. The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

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References

  1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].

    MATH  MathSciNet  ADS  Google Scholar 

  2. D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].

    Article  ADS  Google Scholar 

  3. D. Mateos, String Theory and Quantum Chromodynamics, Class. Quant. Grav. 24 (2007) S713 [arXiv:0709.1523] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. S. Sachdev and M. Mueller, Quantum criticality and black holes, arXiv:0810.3005 [SPIRES].

  5. C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [SPIRES].

    Google Scholar 

  6. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518 [SPIRES].

  8. D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164 (1967) 1776 [SPIRES].

    Article  ADS  Google Scholar 

  10. S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].

    Article  ADS  Google Scholar 

  13. G.W. Gibbons and K.-i. Maeda, Black Holes and Membranes in Higher Dimensional Theories with Dilaton Fields, Nucl. Phys. B 298 (1988) 741 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. D. Garfinkle, G.T. Horowitz and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43 (1991) 3140 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. S. Monni and M. Cadoni, Dilatonic black holes in a S-duality model, Nucl. Phys. B 466 (1996) 101 [hep-th/9511067] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [SPIRES].

    ADS  Google Scholar 

  18. S.S. Gubser, Phase transitions near black hole horizons, Class. Quant. Grav. 22 (2005) 5121 [hep-th/0505189] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. S.S. Gubser and I. Mitra, Instability of charged black holes in anti-de Sitter space, hep-th/0009126 [SPIRES].

  20. S.A. Hartnoll and C.P. Herzog, Impure AdS/CFT, Phys. Rev. D 77 (2008) 106009 [arXiv:0801.1693] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  21. S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  22. K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, arXiv:0911.3586 [SPIRES].

  23. G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].

    Article  ADS  Google Scholar 

  24. S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, arXiv:0912.1061 [SPIRES].

  25. P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  26. G. Dotti and R.J. Gleiser, Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations, Class. Quant. Grav. 22 (2005) L1 [gr-qc/0409005] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. S. Mignemi, Exact solutions of dilaton gravity with (anti)-de Sitter asymptotics, arXiv:0907.0422 [SPIRES].

  29. I.Z. Stefanov, S.S. Yazadjiev and M.D. Todorov, Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics, Mod. Phys. Lett. A 23 (2008) 2915 [arXiv:0708.4141] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [SPIRES].

    ADS  Google Scholar 

  31. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor Superconductivity from Gauge/Gravity Duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [SPIRES].

    Article  ADS  Google Scholar 

  34. R.-G. Cai and Y.-Z. Zhang, Black plane solutions in four-dimensional spacetimes, Phys. Rev. D 54 (1996) 4891 [gr-qc/9609065] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. R.-G. Cai, J.-Y. Ji and K.-S. Soh, Topological dilaton black holes, Phys. Rev. D 57 (1998) 6547 [gr-qc/9708063] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  36. C. Charmousis, B. Gouteraux and J. Soda, Einstein-Maxwell-Dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  37. K. Maeda, M. Natsuume and T. Okamura, Universality class of holographic superconductors, Phys. Rev. D 79 (2009) 126004 [arXiv:0904.1914] [SPIRES].

    ADS  Google Scholar 

  38. S.S. Gubser and F.D. Rocha, The gravity dual to a quantum critical point with spontaneous symmetry breaking, Phys. Rev. Lett. 102 (2009) 061601 [arXiv:0807.1737] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. S.-J. Rey, String theory on thin semiconductors: Holographic realization ofFermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  40. S.-S. Lee, A Non-Fermi Liquid from a Charged Black Hole: A CriticalFermi Ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [SPIRES].

    ADS  Google Scholar 

  41. H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, arXiv:0903.2477 [SPIRES].

  42. M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality,Fermi surfaces and AdS2, arXiv:0907.2694 [SPIRES].

  44. F. Aprile and J.G. Russo, Models of Holographic superconductivity, Phys. Rev. D 81 (2010) 026009 [arXiv:0912.0480] [SPIRES].

    ADS  Google Scholar 

  45. J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett. B 683 (2010) 201 [arXiv:0908.0011] [SPIRES].

    ADS  Google Scholar 

  47. S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  48. J. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [SPIRES].

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari, Cagliari, Italy

    Mariano Cadoni, Giuseppe D’Appollonio & Paolo Pani

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  1. Mariano Cadoni
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  2. Giuseppe D’Appollonio
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  3. Paolo Pani
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Correspondence to Mariano Cadoni.

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ArXiv ePrint: 0912.3520

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Cadoni, M., D’Appollonio, G. & Pani, P. Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime. J. High Energ. Phys. 2010, 100 (2010). https://doi.org/10.1007/JHEP03(2010)100

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  • DOI: https://doi.org/10.1007/JHEP03(2010)100

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