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

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.

arXiv comment24 pages, 1 table, 3 figures

References in corpus (10)

• Black holes and the butterfly effect
• AdS Dual of the Critical O(N) Vector Model
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Stringy gravity, interacting tensionless strings and massless higher spins
• Bounding the Space of Holographic CFTs with Chaos
• Free Large N Supersymmetric Yang-Mills Theory as a String Theory
• Smoothed Transitions in Higher Spin AdS Gravity
• Bulk from Bi-locals in Thermo Field CFT
• The Spectrum of Light States in Large N Minimal Models
• Thermofield Duality for Higher Spin Rindler Gravity

Cited by in corpus (11)

• Summing over Geometries in String Theory
• Thermalization in Large-N CFTs
• Black hole bulk-cone singularities
• Partition function of free conformal fields in 3-plet representation
• Color Confinement and Bose-Einstein Condensation
• Black holes from large N singlet models
• Tidal excitation as mixing in thermal CFT
• Operator thermalisation in $d>2$: Huygens or resurgence
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• Phase transition in complex-time Loschmidt echo of short and long range spin chain
• Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models