Journal of High Energy Physics

, 2013:86 | Cite as

A holographic model of the Kondo effect

  • Johanna Erdmenger
  • Carlos Hoyos
  • Andy O’BannonEmail author
  • Jackson Wu


We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional CFT description, the Kondo effect is a renormalization group flow triggered by a marginally relevant (0+1)-dimensional operator between two fixed points with the same Kac-Moody current algebra. In the large-N limit, with spin SU(N) and charge U(1) symmetries, the Kondo effect appears as a (0+1)-dimensional second-order mean-field transition in which the U(1) charge symmetry is spontaneously broken. Our holographic model, which combines the CFT and large-N descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space, AdS 3, dual to the Kac-Moody current, coupled to a holographic superconductor along an AdS 2 sub-space. Our model exhibits several characteristic features of the Kondo effect, including a dynamically generated scale, a resistivity with power-law behavior in temperature at low temperatures, and a spectral flow producing a phase shift. Our holographic Kondo model may be useful for studying many open problems involving impurities, including for example the Kondo lattice problem.


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


  1. [1]
    J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32 (1964) 37.ADSCrossRefGoogle Scholar
  2. [2]
    C. Rizzuto, Formation of localized moments in metals: experimental bulk properties, Rep. Prog. Phys. 37 (1974) 147.ADSCrossRefGoogle Scholar
  3. [3]
    G. Grüner and A. Zawadowski, Low temperature properties of Kondo alloys, in Progress in low temperature physics, D. Brewer ed., Elsevier, Amsterdam The Netherlands (1978).Google Scholar
  4. [4]
    D. Goldhaber-Gordon et al., Kondo effect in a single-electron transistor, Nature 391 (1998) 156.ADSCrossRefGoogle Scholar
  5. [5]
    S. Cronenwett, T. Oosterkamp and L. Kouwenhoven, A tunable Kondo effect in quantum dots, Science 281 (1998) 540.ADSCrossRefGoogle Scholar
  6. [6]
    W.G. van der Wiel et al., The Kondo effect in the unitary limit, Science 289 (2000) 2105.ADSCrossRefGoogle Scholar
  7. [7]
    K.G. Wilson, The renormalization group: critical phenomena and the Kondo problem, Rev. Mod. Phys. 47 (1975) 773 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    P. Nozières, AFermi-liquiddescription of the Kondo problem at low temperatures, Jour. Low Temp. Phys. 17 (1974) 31.ADSCrossRefGoogle Scholar
  9. [9]
    P. Nozières, The Kondo problem: fancy mathematical techniques versus simple physical ideas, in Low temperature physics conference proceedings, Krusius and Vuorio eds., Elsevier, Amsterdam The Netherlands (1975).Google Scholar
  10. [10]
    N. Andrei, Diagonalization of the Kondo hamiltonian, Phys. Rev. Lett. 45 (1980) 379.ADSCrossRefGoogle Scholar
  11. [11]
    P. Wiegmann, Exact solution of s-d exchange model at T = 0, Sov. Phys. JETP Lett. 31 (1980) 364.ADSGoogle Scholar
  12. [12]
    N. Andrei, K. Furuya and J.H. Lowenstein, Solution of the Kondo problem, Rev. Mod. Phys. 55 (1983) 331.ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    A. Tsvelick and P. Wiegmann, Exact results in the theory of magnetic alloys, Adv. Phys. 32 (1983) 453.ADSCrossRefGoogle Scholar
  14. [14]
    P. Coleman and N. Andrei, Diagonalisation of the Generalised Anderson model, Jour. Phys. C 19 (1986) 3211.ADSGoogle Scholar
  15. [15]
    P. Coleman, Mixed valence as an almost broken symmetry, Phys. Rev. B 35 (1987) 5072.ADSCrossRefGoogle Scholar
  16. [16]
    N. Bickers, Review of techniques in the large-N expansion for dilute magnetic alloys, Rev. Mod. Phys. 59 (1987) 845.ADSCrossRefGoogle Scholar
  17. [17]
    O. Parcollet, A. Georges, G. Kotliar and A. Sengupta, Overscreened multichannel SU(N) Kondo model: large-n solution and conformal field theory, Phys. Rev. B 58 (1998) 3794 [cond-mat/9711192].ADSCrossRefGoogle Scholar
  18. [18]
    I. Affleck, A current algebra approach to the Kondo effect, Nucl. Phys. B 336 (1990) 517 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    I. Affleck and A.W. Ludwig, The Kondo effect, conformal field theory and fusion rules, Nucl. Phys. B 352 (1991) 849 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    I. Affleck and A.W. Ludwig, Critical theory of overscreened Kondo fixed points, Nucl. Phys. B 360 (1991) 641 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    I. Affleck and A.W. Ludwig, Universal nonintegerground state degeneracyin critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    I. Affleck and A. Ludwig, Exact conformal-field-theory results on the multichannel Kondo effect: single-fermion Greens function, self-energy, and resistivity, Phys. Rev. B 48 (1993) 7297.ADSCrossRefGoogle Scholar
  23. [23]
    I. Affleck, Conformal field theory approach to the Kondo effect, Acta Phys. Polon. B 26 (1995) 1869 [cond-mat/9512099] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  24. [24]
    A. Hewson, The Kondo model to heavy fermions, Cambridge University Press, Cambridge U.K. (1993).CrossRefGoogle Scholar
  25. [25]
    D.L. Cox and A. Zawadowski, Exotic kondo effects in metals: Magnetic ions in a crystalline electric field and tunneling centers, Adv. Phys. 47 (1998) 599 [cond-mat/9704103].CrossRefGoogle Scholar
  26. [26]
    S. Doniach, The Kondo lattice and weak anti-ferromagnetism, Physica B+C 91 (1977) 23.Google Scholar
  27. [27]
    H. Tsunetsugu, M. Sigrist, and K. Ueda, The ground-state phase diagram of the one-dimensional Kondo lattice model, Rev. Mod. Phys. 69 (1997) 809.ADSCrossRefGoogle Scholar
  28. [28]
    P. Coleman, Heavy Fermions: electrons at the edge of magnetism, in Handbook of magnetism and advanced magnetic materials: fundamentals and theory, H. Kronmüller and S. Parkin eds., John Wiley and Sons, U.S.A. (2007), cond-mat/0612006.Google Scholar
  29. [29]
    Q. Si, Quantum criticality and the Kondo lattice, in Understanding quantum phase transitions, L.D. Carr ed., CRC Press, U.S.A. (2010), arXiv:1012.5440 [INSPIRE].Google Scholar
  30. [30]
    P. Gegenwart, Q. Si and F. Steglich, Quantum criticality in heavy-fermion metals, Nature Physics 4 (2008) 186 [arXiv:0712.2045].ADSCrossRefGoogle Scholar
  31. [31]
    I. Affleck, N. Laflorencie and E.S. Sorensen, Entanglement entropy in quantum impurity systems and systems with boundaries, J. Phys. A 42 (2009) 4009 [arXiv:0906.1809].MathSciNetzbMATHGoogle Scholar
  32. [32]
    F.B. Anders and A. Schiller, Spin precession and real-time dynamics in the Kondo model: time-dependent numerical renormalization-group study, Phys. Rev. B 74 (2006) 245113 [cond-mat/0604517].ADSCrossRefGoogle Scholar
  33. [33]
    C. Latta et al., Quantum quench of Kondo correlations in optical absorption, Nature 474 (2011) 627 [arXiv:1102.3982].CrossRefGoogle Scholar
  34. [34]
    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] [INSPIRE].
  35. [35]
    S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  36. [36]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  37. [37]
    S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].ADSMathSciNetGoogle Scholar
  38. [38]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S. Kachru, A. Karch and S. Yaida, Adventures in holographic dimer models, New J. Phys. 13 (2011) 035004 [arXiv:1009.3268] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S. Sachdev, Strange metals and the AdS/CFT correspondence, J. Stat. Mech. 1011 (2010) P11022 [arXiv:1010.0682] [INSPIRE].CrossRefGoogle Scholar
  41. [41]
    W. Mueck, The Polyakov loop of anti-symmetric representations as a quantum impurity model, Phys. Rev. D 83 (2011) 066006 [Erratum ibid. D 84 (2011) 129903] [arXiv:1012.1973] [INSPIRE].
  42. [42]
    A. Faraggi and L.A. Pando Zayas, The spectrum of excitations of holographic wIlson loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  43. [43]
    K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].ADSGoogle Scholar
  44. [44]
    N. Karaiskos, K. Sfetsos and E. Tsatis, Brane embeddings in sphere submanifolds, Class. Quant. Grav. 29 (2012) 025011 [arXiv:1106.1200] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  45. [45]
    S. Harrison, S. Kachru and G. Torroba, A maximally supersymmetric Kondo model, Class. Quant. Grav. 29 (2012) 194005 [arXiv:1110.5325] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  46. [46]
    P. Benincasa and A.V. Ramallo, Fermionic impurities in Chern-Simons-matter theories, JHEP 02 (2012) 076 [arXiv:1112.4669] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  47. [47]
    A. Faraggi, W. Mueck and L.A. Pando Zayas, One-loop effective action of the holographic antisymmetric Wilson loop, Phys. Rev. D 85 (2012) 106015 [arXiv:1112.5028] [INSPIRE].ADSGoogle Scholar
  48. [48]
    P. Benincasa and A.V. Ramallo, Holographic Kondo model in various dimensions, JHEP 06 (2012) 133 [arXiv:1204.6290] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    G. Itsios, K. Sfetsos and D. Zoakos, Fermionic impurities in the unquenched ABJM, JHEP 01 (2013) 038 [arXiv:1209.6617] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    H. Matsueda, Multiscale entanglement renormalization ansatz for Kondo problem, arXiv:1208.2872 [INSPIRE].
  51. [51]
    B. Swingle, Entanglement renormalization and holography, Phys. Rev. D 86 (2012) 065007 [arXiv:0905.1317] [INSPIRE].ADSGoogle Scholar
  52. [52]
    B. Swingle, Constructing holographic spacetimes using entanglement renormalization, arXiv:1209.3304 [INSPIRE].
  53. [53]
    T. Senthil, S. Sachdev and M. Vojta, Fractionalized Fermi liquids, Phys. Rev. Lett. 90 (2003) 216403 [cond-mat/0209144].ADSCrossRefGoogle Scholar
  54. [54]
    T. Senthil, M. Vojta and S. Sachdev, Weak magnetism and non-Fermi liquids near heavy-fermion critical points, Phys. Rev. B 69 (2004) 035111 [cond-mat/0305193].ADSCrossRefGoogle Scholar
  55. [55]
    K. Skenderis and M. Taylor, Branes in AdS and pp wave space-times, JHEP 06 (2002) 025 [hep-th/0204054] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    J.A. Harvey and A.B. Royston, Localized modes at a D-brane-O-plane intersection and heterotic Alice atrings, JHEP 04 (2008) 018 [arXiv:0709.1482] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  57. [57]
    E.I. Buchbinder, J. Gomis and F. Passerini, Holographic gauge theories in background fields and surface operators, JHEP 12 (2007) 101 [arXiv:0710.5170] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  58. [58]
    J.A. Harvey and A.B. Royston, Gauge/gravity duality with a chiral N = (0, 8) string defect, JHEP 08 (2008) 006 [arXiv:0804.2854] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    J. Pawelczyk and S.-J. Rey, Ramond-Ramond flux stabilization of D-branes, Phys. Lett. B 493 (2000) 395 [hep-th/0007154] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  60. [60]
    J. Camino, A. Paredes and A. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  61. [61]
    S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    S. Gukov, E. Martinec, G.W. Moore and A. Strominger, Chern-Simons gauge theory and the AdS 3 /CFT 2 correspondence, hep-th/0403225 [INSPIRE].
  64. [64]
    P. Kraus and F. Larsen, Partition functions and elliptic genera from supergravity, JHEP 01 (2007) 002 [hep-th/0607138] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].ADSzbMATHGoogle Scholar
  66. [66]
    K. Jensen, Chiral anomalies and AdS/CMT in two dimensions, JHEP 01 (2011) 109 [arXiv:1012.4831] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  67. [67]
    T. Andrade, J.I. Jottar and R.G. Leigh, Boundary conditions and unitarity: the Maxwell-Chern-Simons system in AdS 3 /CFT 2, JHEP 05 (2012) 071 [arXiv:1111.5054] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  68. [68]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  69. [69]
    M. Berkooz, A. Sever and A. Shomer, ’Double tracedeformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP 04 (2011) 051 [arXiv:1008.1581] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  71. [71]
    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
  72. [72]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  73. [73]
    P. Di Francesco, P. Mathieu, and D. Senechal, Conformal field theory, Springer-Verlag New York Inc., U.S.A. (1997).zbMATHCrossRefGoogle Scholar
  74. [74]
    G. Felder, J. Fröhlich, J. Fuchs and C. Schweigert, Conformal boundary conditions and three-dimensional topological field theory, Phys. Rev. Lett. 84 (2000) 1659 [hep-th/9909140] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  75. [75]
    C. Bachas and M. Gaberdiel, Loop operators and the Kondo problem, JHEP 11 (2004) 065 [hep-th/0411067] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  76. [76]
    A. Alekseev and S. Monnier, Quantization of Wilson loops in Wess-Zumino-Witten models, JHEP 08 (2007) 039 [hep-th/0702174] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  77. [77]
    S. Monnier, Kondo flow invariants, twisted k-theory and Ramond-Ramond charges, JHEP 06 (2008) 022 [arXiv:0803.1565] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  78. [78]
    P. Zinn-Justin and N. Andrei, The generalized multi-channel Kondo model: Thermodynamics and fusion equations, Nucl. Phys. B 528 (1998) 648 [cond-mat/9801158].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  79. [79]
    A. Jerez, N. Andrei and G. Zaránd, Solution of the multichannel Coqblin-Schrieffer impurity model and application to multilevel systems, Phys. Rev. B 58 (1998) 3814 [cond-mat/9803137].ADSCrossRefGoogle Scholar
  80. [80]
    D. Bensimon, A. Jerez, and M. Lavagna, Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models, Phys. Rev. B73 (2006) 224445 [cond-mat/0601144].ADSCrossRefGoogle Scholar
  81. [81]
    E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  82. [82]
    J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  83. [83]
    S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  84. [84]
    N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  85. [85]
    J. Gomis and F. Passerini, Wilson loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  86. [86]
    E. Gava, K. Narain and M. Sarmadi, On the bound states of p-branes and (p + 2)-branes, Nucl. Phys. B 504 (1997) 214 [hep-th/9704006] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  87. [87]
    M. Aganagic, R. Gopakumar, S. Minwalla and A. Strominger, Unstable solitons in noncommutative gauge theory, JHEP 04 (2001) 001 [hep-th/0009142] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  88. [88]
    J. Polchinski, String theory. Vol. 2: superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998).zbMATHCrossRefGoogle Scholar
  89. [89]
    E. Pomoni and L. Rastelli, Large-N field theory and AdS tachyons, JHEP 04 (2009) 020 [arXiv:0805.2261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  90. [90]
    E. Pomoni and L. Rastelli, Intersecting flavor branes, JHEP 10 (2012) 171 [arXiv:1002.0006] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  91. [91]
    D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [INSPIRE].ADSzbMATHGoogle Scholar
  92. [92]
    K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    D. Kutasov, J. Lin and A. Parnachev, Conformal phase transitions at weak and strong coupling, Nucl. Phys. B 858 (2012) 155 [arXiv:1107.2324] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  94. [94]
    N. Iqbal, H. Liu and M. Mezei, Quantum phase transitions in semi-local quantum liquids, arXiv:1108.0425 [INSPIRE].
  95. [95]
    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  96. [96]
    T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  97. [97]
    R. Casero, E. Kiritsis and A. Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys. B 787 (2007) 98 [hep-th/0702155] [INSPIRE].ADSCrossRefGoogle Scholar
  98. [98]
    O. Bergman, S. Seki and J. Sonnenschein, Quark mass and condensate in HQCD, JHEP 12 (2007) 037 [arXiv:0708.2839] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    A. Dhar and P. Nag, Sakai-Sugimoto model, tachyon condensation and chiral symmetry breaking, JHEP 01 (2008) 055 [arXiv:0708.3233] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  100. [100]
    D. Marolf and S.F. Ross, Boundary conditions and new dualities: vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].ADSCrossRefGoogle Scholar
  101. [101]
    A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS 2 black holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].ADSCrossRefGoogle Scholar
  102. [102]
    I. Papadimitriou, Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  103. [103]
    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  104. [104]
    S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [INSPIRE].ADSGoogle Scholar
  105. [105]
    G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  106. [106]
    J.L. Davis, M. Gutperle, P. Kraus and I. Sachs, Stringy NJLS and Gross-Neveu models at finite density and temperature, JHEP 10 (2007) 049 [arXiv:0708.0589] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  107. [107]
    D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].ADSCrossRefGoogle Scholar
  108. [108]
    K. Hashimoto and N. Iizuka, Impurities in holography and transport coefficients, arXiv:1207.4643 [INSPIRE].
  109. [109]
    T. Ishii and S.-J. Sin, Impurity effect in a holographic superconductor, JHEP 04 (2013) 128 [arXiv:1211.1798] [INSPIRE].ADSCrossRefGoogle Scholar
  110. [110]
    D. Freedman, S. Gubser, K. Pilch and N. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].MathSciNetzbMATHCrossRefGoogle Scholar
  111. [111]
    M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  112. [112]
    A. Green, An introduction to gauge gravity duality and its application in condensed matter, Contemp. Phys. 54 (2013) 33 [arXiv:1304.5908] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Johanna Erdmenger
    • 1
  • Carlos Hoyos
    • 2
  • Andy O’Bannon
    • 3
    • 4
    Email author
  • Jackson Wu
    • 5
  1. 1.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  2. 2.Raymond and Beverly Sackler School of Physics and AstronomyTel-Aviv UniversityRamat-AvivIsrael
  3. 3.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUnited Kingdom
  4. 4.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordUnited Kingdom
  5. 5.National Center for Theoretical Sciences, Physics DivisionHsinchuChina

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