Advertisement

Transitions in dilaton holography with global or local symmetries

  • Alberto Salvio
Article

Abstract

We study various transitions in dilaton holography, including those associated with the spontaneous breaking of a global (superfluid case) or local (superconductor case) U(1) symmetry in diverse dimensions d. By analyzing the thermodynamics of the dilaton-gravity system we find that scale invariance is broken at low temperatures, as shown by a nontrivial hyperscaling violation exponent in the infrared; increasing the temperature we recover scale symmetry in a d dependent way: while for d = 2 + 1 a phase transition is found, for d = 3 + 1 the transition is rather a crossover. This is the expected behavior of QCD where the number of colors N c equals three (although in our holographic calculations N c → ∞). When the U(1) is preserved and at low temperatures, the system is insulating for arbitrary d if the dilaton is appropriately coupled to the gauge field; for other couplings we also find a linear in temperature resistivity. We then determine the prediction of these models for several quantities in the superconducting phase: the DC and AC conductivity, the gap for charged excitations, the superfluid density, the vortex profiles, the coherence length, the penetration depth and the critical magnetic fields. We show that at low temperatures some of these quantities differ qualitatively compared with the corresponding models without the dilaton, although the superconductor is robustly of Type II. The ratio of the gap over the critical temperature of the superconductor is studied in detail varying d and the couplings of the dilaton and then compared with the BCS value. A holographic renormalization is required in d > 2 + 1 to compute some quantities (such as the AC conductivity and the penetration depth) and we explain in detail how to perform it.

Keywords

Gauge-gravity correspondence Spontaneous Symmetry Breaking AdS-CFT 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]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].Google Scholar
  3. [3]
    S.A. Hartnoll, Quantum critical dynamics from black holes, arXiv:0909.3553 [INSPIRE].
  4. [4]
    S. Sachdev, Condensed matter and AdS/CFT, Lect. Notes Phys. 828 (2011) 273 [arXiv:1002.2947] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    A. Pires, Ads/CFT correspondence in condensed matter, arXiv:1006.5838 [INSPIRE].
  6. [6]
    G.T. Horowitz, Surprising connections between general relativity and condensed matter, Class. Quant. Grav. 28 (2011) 114008 [arXiv:1010.2784] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
  8. [8]
    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] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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
  12. [12]
    G.T. Horowitz and M.M. Roberts, Holographic superconductors with various condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].ADSGoogle Scholar
  13. [13]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    P.A. Lee, N. Nagaosa and X.G. Wen, Doping a mott insulator: physics of high temperature superconductivity, Rev. Mod. Phys. 78 (2006) 17.ADSCrossRefGoogle Scholar
  15. [15]
    A. Salvio, Holographic superfluids and superconductors in dilaton-gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, arXiv:1212.2625 [INSPIRE].
  17. [17]
    J. Gath, J. Hartong, R. Monteiro and N.A. Obers, Holographic models for theories with hyperscaling violation, arXiv:1212.3263.
  18. [18]
    O. Domenech, M. Montull, A. Pomarol, A. Salvio and P.J. Silva, Emergent gauge fields in holographic superconductors, JHEP 08 (2010) 033 [arXiv:1005.1776] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Anabalon, Exact black holes and universality in the backreaction of non-linear σ-models with a potential in (A)dS 4, JHEP 06 (2012) 127 [arXiv:1204.2720] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    A. Acena, A. Anabalon and D. Astefanesei, Exact hairy black brane solutions in AdS 5 and holographic RG flows, arXiv:1211.6126 [INSPIRE].
  21. [21]
    M. Montull, A. Pomarol and P.J. Silva, The holographic superconductor vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].ADSGoogle Scholar
  24. [24]
    K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev. D 78 (2008) 106006 [arXiv:0809.3079] [INSPIRE].MathSciNetADSGoogle Scholar
  25. [25]
    X.-H. Ge, B. Wang, S.-F. Wu and G.-H. Yang, Analytical study on holographic superconductors in external magnetic field, JHEP 08 (2010) 108 [arXiv:1002.4901] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M. Montull, O. Pujolàs, A. Salvio and P.J. Silva, Flux periodicities and quantum hair on holographic superconductors, Phys. Rev. Lett. 107 (2011) 181601 [arXiv:1105.5392] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Montull, O. Pujolàs, A. Salvio and P.J. Silva, Magnetic response in the holographic insulator/superconductor transition, JHEP 04 (2012) 135 [arXiv:1202.0006] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    A. Salvio, Superconductivity, superfluidity and holography, arXiv:1301.0201 [INSPIRE].
  29. [29]
    E. Witten, SL(2, \( \mathbb{Z} \)) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
  30. [30]
    S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett. B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].ADSGoogle Scholar
  33. [33]
    M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor superconductivity from gauge/gravity duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic superconductor/insulator transition at zero temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    G.T. Horowitz and B. Way, Complete phase diagrams for a holographic superconductor/insulator system, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    J.M. Murray and Z. Tesanovic, Isolated vortex and vortex lattice in a holographic p-wave superconductor, Phys. Rev. D 83 (2011) 126011 [arXiv:1103.3232] [INSPIRE].ADSGoogle Scholar
  37. [37]
    X. Gao, M. Kaminski, H.-B. Zeng and H.-Q. Zhang, Non-equilibrium field dynamics of an honest holographic superconductor, JHEP 11 (2012) 112 [arXiv:1204.3103] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett. 56 (1986) 416 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].ADSGoogle Scholar
  40. [40]
    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    J.M. Pawlowski, The QCD phase diagram: results and challenges, AIP Conf. Proc. 1343 (2011) 75 [arXiv:1012.5075] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    B. Lucini, M. Teper and U. Wenger, The deconfinement transition in SU(N) gauge theories, Phys. Lett. B 545 (2002) 197 [hep-lat/0206029] [INSPIRE].MathSciNetADSGoogle Scholar
  43. [43]
    B. Lucini, M. Teper and U. Wenger, The high temperature phase transition in SU(N) gauge theories, JHEP 01 (2004) 061 [hep-lat/0307017] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    B. Lucini, M. Teper and U. Wenger, Properties of the deconfining phase transition in SU(N) gauge theories, JHEP 02 (2005) 033 [hep-lat/0502003] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  45. [45]
    M. Alishahiha, M.R.M. Mozaffar and A. Mollabashi, Holographic aspects of two-charged dilatonic black hole in AdS 5, JHEP 10 (2012) 003 [arXiv:1208.2535] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    A. Donos and S.A. Hartnoll, Universal linear in temperature resistivity from black hole superradiance, Phys. Rev. D 86 (2012) 124046 [arXiv:1208.4102] [INSPIRE].ADSGoogle Scholar
  47. [47]
    T. Albash and C.V. Johnson, Phases of holographic superconductors in an external magnetic field, arXiv:0906.0519 [INSPIRE].
  48. [48]
    T. Albash and C.V. Johnson, Vortex and droplet engineering in holographic superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].ADSGoogle Scholar
  49. [49]
    W.H. Kleiner, L.M. Roth and S.H. Autler, Bulk solution of Ginzburg-Landau equations for type II superconductors: upper critical field region, Phys. Rev. A 133 (1964) 1226.ADSCrossRefGoogle Scholar
  50. [50]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Departamento de Física TeóricaUniversidad Autónoma de Madrid and Instituto de Física Teórica IFT-UAM/CSICMadridSpain

Personalised recommendations