Abstract
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.
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References
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Cubic Interaction in Extended Theories of Massless Higher Spin Fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].
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].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
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].
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
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].
S. Banerjee et al., Smoothed Transitions in Higher Spin AdS Gravity, Class. Quant. Grav. 30 (2013) 104001 [arXiv:1209.5396] [INSPIRE].
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].
K. Furuuchi, From free fields to AdS: Thermal case, Phys. Rev. D 72 (2005) 066009 [hep-th/0505148] [INSPIRE].
A. Jevicki and J. Yoon, Bulk from Bi-locals in Thermo Field CFT, JHEP 02 (2016) 090 [arXiv:1503.08484] [INSPIRE].
A. Jevicki and K. Suzuki, Thermofield Duality for Higher Spin Rindler Gravity, JHEP 02 (2016) 094 [arXiv:1508.07956] [INSPIRE].
S. Giombi, TASI Lectures on the Higher Spin-CFT duality, arXiv:1607.02967 [INSPIRE].
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].
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].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
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].
E. Perlmutter, Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE].
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ArXiv ePrint: 1612.03009
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Amado, I., Sundborg, B., Thorlacius, L. et al. Probing emergent geometry through phase transitions in free vector and matrix models. J. High Energ. Phys. 2017, 5 (2017). https://doi.org/10.1007/JHEP02(2017)005
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DOI: https://doi.org/10.1007/JHEP02(2017)005