Journal of High Energy Physics

, 2011:104 | Cite as

Holographic symmetry-breaking phases in AdS3/CFT2

  • Nima Lashkari


In this note we study the symmetry-breaking phases of 3D gravity coupled to matter. In particular, we consider black holes with scalar hair as a model of symmetrybreaking phases of a strongly coupled 1 + 1 dimensional CFT. In the case of a discrete symmetry, we show that these theories admit phases of broken symmetry and study the thermodynamics of these phases. We also demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry breaking at low temperature. The apparent contradiction with the Coleman-Mermin-Wagner theorem is discussed.


Gauge-gravity correspondence Spontaneous Symmetry Breaking Holography and condensed matter physics (AdS/CMT) 


  1. [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) 1133] [hep-th/9711200] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  2. [2]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetMATHGoogle Scholar
  3. [3]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].Google Scholar
  6. [6]
    S.S. Gubser and I. Mitra, Instability of charged black holes in Anti-de Sitter space, hep-th/0009126 [INSPIRE].
  7. [7]
    S.S. Gubser and I. Mitra, The Evolution of unstable black holes in anti-de Sitter space, JHEP 08 (2001) 018 [hep-th/0011127] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    S.S. Gubser, Phase transitions near black hole horizons, Class. Quant. Grav. 22 (2005) 5121 [hep-th/0505189] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  9. [9]
    F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009)126008 [arXiv:0901.1160] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    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
  11. [11]
    G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].ADSGoogle Scholar
  12. [12]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008)015 [arXiv:0810.1563] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  14. [14]
    M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2 + 1 gravity coupled to a scalar field, Phys. Rev. D 65 (2002) 104007 [hep-th/0201170] [INSPIRE].MathSciNetADSGoogle Scholar
  15. [15]
    C. Martinez, C. Teitelboim and J. Zanelli, Charged rotating black hole in three space-time dimensions, Phys. Rev. D 61 (2000) 104013 [hep-th/9912259] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  17. [17]
    D. Maity, S. Sarkar, N. Sircar, B. Sathiapalan and R. Shankar, Properties of CFTs dual to Charged BTZ black-hole, Nucl. Phys. B 839 (2010) 526 [arXiv:0909.4051] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    N. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17 (1966) 1133 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    P. Hohenberg, Existence of Long-Range Order in One and Two Dimensions, Phys. Rev. 158 (1967)383 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S.R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31 (1973)259 [INSPIRE].ADSMATHCrossRefGoogle Scholar
  21. [21]
    E. Witten, Chiral Symmetry, the 1/n Expansion and the SU(N ) Thirring Model, Nucl. Phys. B 145 (1978) 110 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    D. Anninos, S.A. Hartnoll and N. Iqbal, Holography and the Coleman-Mermin-Wagner theorem, Phys. Rev. D 82 (2010) 066008 [arXiv:1005.1973] [INSPIRE].ADSGoogle Scholar
  23. [23]
    J. Ren, One-dimensional holographic superconductor from AdS 3 /CF T 2 correspondence, JHEP 11 (2010) 055 [arXiv:1008.3904] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    A. Buchel and C. Pagnutti, Exotic Hairy Black Holes, Nucl. Phys. B 824 (2010) 85 [arXiv:0904.1716] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    A. Chubukov, Order from disorder in a kagome antiferromagnet, Phys. Rev. Lett 69 (1992) 832.ADSCrossRefGoogle Scholar
  27. [27]
    J. Gegenberg, C. Martinez and R. Troncoso, A Finite action for three-dimensional gravity with a minimally coupled scalar field, Phys. Rev. D 67 (2003) 084007 [hep-th/0301190] [INSPIRE].MathSciNetADSGoogle Scholar
  28. [28]
    D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    A. Buchel and C. Pagnutti, Correlated stability conjecture revisited, Phys. Lett. B 697 (2011) 168 [arXiv:1010.5748] [INSPIRE].ADSGoogle Scholar
  30. [30]
    K. Skenderis and M. Taylor, Fuzzball solutions and D1 − D5 microstates, Phys. Rev. Lett. 98 (2007)071601 [hep-th/0609154] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].ADSMATHCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.McGill Physics DepartmentMontréalCanada

Personalised recommendations