Probing emergent geometry through phase transitions in free vector and matrix models

  • Irene Amado
  • Bo Sundborg
  • Larus Thorlacius
  • Nico Wintergerst
Open Access
Regular Article - Theoretical Physics


Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N ) or U(N ) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing ’t Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.


AdS-CFT Correspondence Black Holes in String Theory Higher Spin Gravity Confinement 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    E.S. Fradkin and M.A. Vasiliev, Cubic Interaction in Extended Theories of Massless Higher Spin Fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].ADSGoogle Scholar
  5. [5]
    P. Haggi-Mani and B. Sundborg, Free large-N supersymmetric Yang-Mills theory as a string theory, JHEP 04 (2000) 031 [hep-th/0002189] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
  9. [9]
    S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    S. Banerjee et al., Smoothed Transitions in Higher Spin AdS Gravity, Class. Quant. Grav. 30 (2013) 104001 [arXiv:1209.5396] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    M.R. Gaberdiel, R. Gopakumar and M. Rangamani, The Spectrum of Light States in Large-N Minimal Models, JHEP 01 (2014) 116 [arXiv:1310.1744] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    K. Furuuchi, From free fields to AdS: Thermal case, Phys. Rev. D 72 (2005) 066009 [hep-th/0505148] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    A. Jevicki and J. Yoon, Bulk from Bi-locals in Thermo Field CFT, JHEP 02 (2016) 090 [arXiv:1503.08484] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    A. Jevicki and K. Suzuki, Thermofield Duality for Higher Spin Rindler Gravity, JHEP 02 (2016) 094 [arXiv:1508.07956] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Giombi, TASI Lectures on the Higher Spin-CFT duality, arXiv:1607.02967 [INSPIRE].
  17. [17]
    O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    D.J. Gross and E. Witten, Possible Third Order Phase Transition in the Large-N Lattice Gauge Theory, Phys. Rev. D 21 (1980) 446 [INSPIRE].ADSGoogle Scholar
  19. [19]
    S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    G. Dvali, D. Flassig, C. Gomez, A. Pritzel and N. Wintergerst, Scrambling in the Black Hole Portrait, Phys. Rev. D 88 (2013) 124041 [arXiv:1307.3458] [INSPIRE].ADSGoogle Scholar
  21. [21]
    E. Perlmutter, Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Irene Amado
    • 1
  • Bo Sundborg
    • 1
  • Larus Thorlacius
    • 1
    • 2
  • Nico Wintergerst
    • 1
  1. 1.The Oskar Klein Centre for Cosmoparticle Physics, Department of PhysicsStockholm UniversityStockholmSweden
  2. 2.Science InstituteUniversity of IcelandReykjavikIceland

Personalised recommendations