Generalized Hawking-Page transitions

Abstract

We construct holographic backgrounds that are dual by the AdS/CFT correspondence to Euclidean conformal field theories on products of spheres $S^{d_1}\times S^{d_2}$, for conformal field theories whose dual may be approximated by classical Einstein gravity (typically these are large $N$ strongly coupled theories). For $d_2=1$ these backgrounds correspond to thermal field theories on $S^{d_1}$, and Hawking and Page found that there are several possible bulk solutions, with two different topologies, that compete with each other, leading to a phase transition as the relative size of the spheres is modified. By numerically solving the Einstein equations we find similar results also for $d_2>1$, with bulk solutions in which either one or the other sphere shrinks to zero smoothly at a minimal value of the radial coordinate, and with a first order phase transition (for $d_1+d_2<9$) between solutions of two different topologies as the relative radius changes. For a critical ratio of the radii there is a (sub-dominant) singular solution where both spheres shrink, and we analytically analyze the behavior near this radius. For $d_1+d_2<9$ the number of solutions grows to infinity as the critical ratio is approached.

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• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Localization techniques in quantum field theories
• Topology change in General Relativity and the black-hole black-string transition
• Critical behavior of the black hole / black string transition
• Acceleration-Induced Deconfinement Transitions in de Sitter Spacetime

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• Revisiting Coleman-de Luccia transitions in the AdS regime using holography
• The entanglement entropy of typical pure states and replica wormholes
• An infinity of black holes
• Little String Theories on Curved Manifolds
• Holographic CFTs on $Ad{S}_d\times S^n$ and conformal defects
• Partition functions on squashed seven-spheres and holography