Emergent gauge fields in holographic superconductors



Holographic superconductors have been studied so far in the absence of dynamical electromagnetic fields, namely in the limit in which they coincide with holographic superfluids. It is possible, however, to introduce dynamical gauge fields if a Neumann-type boundary condition is imposed on the AdS-boundary. In 3 + 1 dimensions, the dual theory is a 2 + 1 dimensional CFT whose spectrum contains a massless gauge field, signaling the emergence of a gauge symmetry. We study the impact of a dynamical gauge field in vortex configurations where it is known to significantly affect the energetics and phase transitions. We calculate the critical magnetic fields H c1 and H c2, obtaining that holographic superconductors are of Type II (H c1 < H c2). We extend the study to 4 + 1 dimensions where the gauge field does not appear as an emergent phenomenon, but can be introduced, by a proper renormalization, as an external dynamical field. We also compare our predictions with those arising from a Ginzburg-Landau theory and identify the generic properties of Abrikosov vortices in holographic models.


Spontaneous Symmetry Breaking AdS-CFT Correspondence Gauge Symmetry 


  1. [1]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    For a review see, for example, S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].
  3. [3]
    See also, C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [SPIRES].
  4. [4]
    See also, G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722 [SPIRES].
  5. [5]
    P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: Vector Hair for an AdS Black Hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [SPIRES].ADSGoogle Scholar
  6. [6]
    C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [SPIRES].
  8. [8]
    N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    V.L. Ginzburg and L.D. Landau, On the Theory of superconductivity, Zh. Eksp. Teor. Fiz. 20 (1950) 1064 [SPIRES]. Google Scholar
  10. [10]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    T. Albash and C.V. Johnson, A Holographic Superconductor in an External Magnetic Field, JHEP 09 (2008) 121 [arXiv:0804.3466] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [SPIRES].ADSGoogle Scholar
  13. [13]
    K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev. D 78 (2008) 106006 [arXiv:0809.3079] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    X.-H. Ge, B. Wang, S.-F. Wu and G.-H. Yang, Analytical study on holographic superconductors in external magnetic field, arXiv:1002.4901 [SPIRES].
  15. [15]
    M. Montull, A. Pomarol and P.J. Silva, The Holographic Superconductor Vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Inhomogeneous Structures in Holographic Superfluids: II. Vortices, Phys. Rev. D 81 (2010) 126012 [arXiv:0912.4280] [SPIRES]. ADSGoogle Scholar
  17. [17]
    T. Albash and C.V. Johnson, Phases of Holographic Superconductors in an External Magnetic Field, arXiv:0906.0519 [SPIRES].
  18. [18]
    T. Albash and C.V. Johnson, Vortex and Droplet Engineering in Holographic Superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [SPIRES].ADSGoogle Scholar
  19. [19]
    S. Weinberg, Superconductivity For Particular Theorists, Prog. Theor. Phys. Suppl. 86 (1986) 43 [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    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. CrossRefADSGoogle Scholar
  21. [21]
    G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [SPIRES].ADSGoogle Scholar
  22. [22]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  23. [23]
  24. [24]
    K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [SPIRES].ADSGoogle Scholar
  25. [25]
    B.D. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1 (1962) 251 [SPIRES].MATHCrossRefADSGoogle Scholar
  26. [26]
    S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [SPIRES].CrossRefGoogle Scholar
  28. [28]
    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] [SPIRES].ADSGoogle Scholar
  29. [29]
    M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor Superconductivity from Gauge/Gravity Duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  30. [30]
    K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  31. [31]
    S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].MathSciNetADSGoogle Scholar
  32. [32]
    M. Taylor, Non-relativistic holography, arXiv:0812.0530 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Departament de Física and IFAEUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Institut de Ciències de l’Espai (CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC/CSIC)Universitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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