Advertisement

Minimal holographic superconductors from maximal supergravity

  • Nikolay Bobev
  • Arnab Kundu
  • Krzysztof Pilch
  • Nicholas P. Warner
Article

Abstract

We study a truncation of four-dimensional maximal gauged supergravity that provides a realization of the minimal model of a holographic superconductor. We find various flow solutions in this truncation at zero and finite temperature with a non-trivial profile for the charged scalar. Below a critical temperature we find holographic superconductor solutions that represent the thermodynamically preferred phase. Depending on the choice of boundary conditions, the superconducting phase transition is either first or second order. For vanishing temperature we find a flow with a condensing charged scalar that interpolates between two perturbatively stable AdS4 vacua and is the zero-temperature ground state of the holographic superconductor.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 

References

  1. [1]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].Google Scholar
  3. [3]
    G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [INSPIRE].
  4. [4]
    S.S. Gubser, Breaking an abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  5. [5]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].MathSciNetADSGoogle Scholar
  8. [8]
    S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    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] [INSPIRE].MathSciNetADSGoogle Scholar
  11. [11]
    J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    A. Donos and J.P. Gauntlett, Superfluid black branes in AdS 4 × S 7, JHEP 06 (2011) 053 [arXiv:1104.4478] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    F. Aprile, D. Roest and J.G. Russo, Holographic superconductors from gauged supergravity, JHEP 06 (2011) 040 [arXiv:1104.4473] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity instabilities of non-supersymmetric quantum critical points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    T. Fischbacher, K. Pilch and N.P. Warner, New supersymmetric and stable, non-supersymmetric phases in supergravity and holographic field theory, arXiv:1010.4910 [INSPIRE].
  16. [16]
    N. Warner, Some properties of the scalar potential in gauged supergravity theories, Nucl. Phys. B 231 (1984) 250 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    N. Warner, Some new extrema of the scalar potential of gauged N = 8 supergravity, Phys. Lett. B 128 (1983) 169 [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    N. Bobev, A. Kundu, K. Pilch and N.P. Warner, to appear.Google Scholar
  19. [19]
    T. Fischbacher, Fourteen new stationary points in the scalar potential of SO(8)-gauged N = 8, D = 4 supergravity,JHEP 09 (2010) 068 [arXiv:0912.1636] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    T. Fischbacher, The encyclopedic reference of critical points for SO(8)-gauged N = 8 supergravity. Part 1: cosmological constants in the range −Λ/g 2 ∈ [6, 14.7), arXiv:1109.1424 [INSPIRE].
  21. [21]
    S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A general class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    S. Franco, A.M. Garcia-Garcia and D. Rodriguez-Gomez, A holographic approach to phase transitions, Phys. Rev. D 81 (2010) 041901 [arXiv:0911.1354] [INSPIRE].MathSciNetADSGoogle Scholar
  23. [23]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    B. de Wit and H. Nicolai, Extended supergravity with local SO(5) invariance, Nucl. Phys. B 188 (1981) 98 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  27. [27]
    K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].MathSciNetMATHCrossRefGoogle Scholar
  28. [28]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [INSPIRE].ADSGoogle Scholar
  30. [30]
    G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  33. [33]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  34. [34]
    M. Berkooz, A. Sever and A. Shomer, ’Double tracedeformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    S. Weinberg, Superconductivity for particular theorists, Prog. Theor. Phys. Suppl. 86 (1986) 43 [INSPIRE].
  36. [36]
    N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Holographic, N = 1 supersymmetric RG flows on M 2 branes, JHEP 09 (2009) 043 [arXiv:0901.2736] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Nikolay Bobev
    • 1
  • Arnab Kundu
    • 2
  • Krzysztof Pilch
    • 3
  • Nicholas P. Warner
    • 3
  1. 1.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookU.S.A.
  2. 2.Theory Group, Department of PhysicsUniversity of Texas at AustinAustinU.S.A.
  3. 3.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesU.S.A.

Personalised recommendations