Holographic description of the phase diagram of a chiral symmetry breaking gauge theory

  • Nick Evans
  • Astrid Gebauer
  • Keun-Young KimEmail author
  • Maria Magou


The large N \( \mathcal{N} = 4 \) gauge theory with quenched \( \mathcal{N} = 2 \) quark matter in the presence of a magnetic field displays chiral symmetry breaking. We study the temperature and chemical potential dependence of this theory using its gravity dual (based on the D3/D7 brane system). With massless quarks, at zero chemical potential, the theory displays a first order thermal transition where chiral symmetry is restored and simultaneously the mesons of the theory melt. At zero temperature, these transitions with chemical potential are second order and occur at different chemical potential values. Between the three there are two tri-critical points, the positions of which we identify. At finite quark mass the second order transition for chiral symmetry becomes a cross over and there is a critical point at the end of the first order transition, while the meson melting transition remains similar to the massless quark case. We track the movement of the critical points as the mass is raised relative to the magnetic field.


Gauge-gravity correspondence AdS-CFT Correspondence QCD 


  1. [1]
    K. Rajagopal and F. Wilczek, The condensed matter physics of QCD, hep-ph/0011333 [SPIRES].
  2. [2]
    M.A. Stephanov, QCD phase diagram: An overview, PoS(LAT2006)024 [hep-lat/0701002] [SPIRES].
  3. [3]
    O. Philipsen, Towards a determination of the chiral critical surface of QCD, arXiv:0910.0785 [SPIRES].
  4. [4]
    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] [SPIRES].zbMATHMathSciNetADSGoogle Scholar
  5. [5]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].zbMATHMathSciNetGoogle Scholar
  6. [6]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    M. Graña and J. Polchinski, Gauge-gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [SPIRES].ADSGoogle Scholar
  9. [9]
    M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda and R. Marotta, N = 2 gauge theories on systems of fractional D3/D7 branes, Nucl. Phys. B 621 (2002) 157 [hep-th/0107057] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavour, JHEP 07 (2003) 049 [hep-th/0304032] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [SPIRES].ADSGoogle Scholar
  12. [12]
    S. Nakamura, Y. Seo, S.-J. Sin and K.P. Yogendran, A new phase at finite quark density from AdS/CFT, J. Korean Phys. Soc. 52 (2008) 1734 [hep-th/0611021] [SPIRES].CrossRefGoogle Scholar
  13. [13]
    S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    S. Nakamura, Y. Seo, S.-J. Sin and K.P. Yogendran, Baryon-charge Chemical Potential in AdS/CFT, Prog. Theor. Phys. 120 (2008) 51 [arXiv:0708.2818] [SPIRES].zbMATHCrossRefADSGoogle Scholar
  15. [15]
    A. Karch and A. O’Bannon, Holographic Thermodynamics at Finite Baryon Density: Some Exact Results, JHEP 11 (2007) 074 [arXiv:0709.0570] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv:0709.1225] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    K. Ghoroku, M. Ishihara and A. Nakamura, D3/D7 holographic Gauge theory and Chemical potential, Phys. Rev. D 76 (2007) 124006 [arXiv:0708.3706] [SPIRES].MathSciNetADSGoogle Scholar
  18. [18]
    K. Peeters, J. Sonnenschein and M. Zamaklar, Holographic melting and related properties of mesons in a quark gluon plasma, Phys. Rev. D 74 (2006) 106008 [hep-th/0606195] [SPIRES].ADSGoogle Scholar
  19. [19]
    C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Holographic Meson Melting, JHEP 04 (2007) 031 [hep-th/0612169] [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    J. Erdmenger, M. Kaminski and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev. D 77 (2008) 046005 [arXiv:0710.0334] [SPIRES].ADSGoogle Scholar
  21. [21]
    J. Erdmenger et al., Quasinormal modes of massive charged flavor branes, arXiv:0911.3544 [SPIRES].
  22. [22]
    V.G. Filev, C.V. Johnson, R.C. Rashkov and K.S. Viswanathan, Flavoured large-N gauge theory in an external magnetic field, JHEP 10 (2007) 019 [hep-th/0701001] [SPIRES].CrossRefADSGoogle Scholar
  23. [23]
    T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Finite Temperature Large-N Gauge Theory with Quarks in an External Magnetic Field, JHEP 07 (2008) 080 [arXiv:0709.1547] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    V.G. Filev, Criticality, Scaling and Chiral Symmetry Breaking in External Magnetic Field,JHEP 04 (2008) 088 [arXiv:0706.3811] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    V.G. Filev and C.V. Johnson, Universality in the Large N c Dynamics of Flavour: Thermal Vs. Quantum Induced Phase Transitions, JHEP 10 (2008) 058 [arXiv:0805.1950] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    V.G. Filev, Hot Defect Superconformal Field Theory in an External Magnetic Field, JHEP 11 (2009) 123 [arXiv:0910.0554] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    A.V. Zayakin, QCD Vacuum Properties in a Magnetic Field from AdS/CFT: Chiral Condensate and Goldstone Mass, JHEP 07 (2008) 116 [arXiv:0807.2917] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  29. [29]
    V.G. Filev, C.V. Johnson and J.P. Shock, Universal Holographic Chiral Dynamics in an External Magnetic Field, JHEP 08 (2009) 013 [arXiv:0903.5345] [SPIRES].CrossRefADSGoogle Scholar
  30. [30]
    S.S. Gubser, Dilaton-driven confinement, hep-th/9902155 [SPIRES].
  31. [31]
    L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The supergravity dual of N = 1 super Yang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  32. [32]
    K.-Y. Kim, S.-J. Sin and I. Zahed, Dense hadronic matter in holographic QCD, hep-th/0608046 [SPIRES].
  33. [33]
    K.-Y. Kim, S.-J. Sin and I. Zahed, The Chiral Model of Sakai-Sugimoto at Finite Baryon Density, JHEP 01 (2008) 002 hep-th/0708.1469 [SPIRES].CrossRefADSGoogle Scholar
  34. [34]
    J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in non-supersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [SPIRES].MathSciNetADSGoogle Scholar
  35. [35]
    R. Apreda, J. Erdmenger, N. Evans and Z. Guralnik, Strong coupling effective Higgs potential and a first order thermal phase transition from AdS/CFT duality, Phys. Rev. D 71 (2005) 126002 [hep-th/0504151] [SPIRES].ADSGoogle Scholar
  36. [36]
    T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, A topology-changing phase transition and the dynamics of flavour, Phys. Rev. D 77 (2008) 066004 [hep-th/0605088] [SPIRES].ADSGoogle Scholar
  37. [37]
    D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  38. [38]
    D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  39. [39]
    S. Nakamura, Comments on Chemical Potentials in AdS/CFT, Prog. Theor. Phys. 119 (2008) 839 [arXiv:0711.1601] [SPIRES].zbMATHCrossRefADSGoogle Scholar
  40. [40]
    Y. Seo, J.P. Shock, S.-J. Sin and D. Zoakos, Holographic Hadrons in a Confining Finite Density Medium, arXiv:0912.4013 [SPIRES].
  41. [41]
    P. de Forcrand and O. Philipsen, The chiral critical point of Nf = 3 QCD at finite density to the order (mu/T)4, JHEP 11 (2008) 012 [arXiv:0808.1096] [SPIRES].CrossRefGoogle Scholar
  42. [42]
    P. de Forcrand and O. Philipsen, The chiral critical line of N f = 2 + 1 QCD at zero and nonzero baryon density, JHEP 01 (2007) 077 [hep-lat/0607017] [SPIRES].CrossRefGoogle Scholar
  43. [43]
    J. Langelage and O. Philipsen, The deconfinement transition of finite density QCD with heavy quarks from strong coupling series, arXiv:0911.2577 [SPIRES].
  44. [44]
    S. Kim, P. de Forcrand, S. Kratochvila and T. Takaishi, The 3-state Potts model as a heavy quark finite density laboratory, PoS(LAT2005)166 [hep-lat/0510069] [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Nick Evans
    • 1
  • Astrid Gebauer
    • 1
  • Keun-Young Kim
    • 1
    Email author
  • Maria Magou
    • 1
  1. 1.School of Physics and AstronomyUniversity of SouthamptonSouthamptonU.K.

Personalised recommendations