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 d2 = 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 d2> 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 d1 + d2< 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 d1 + d2< 9 the number of solutions grows to infinity as the critical ratio is approached.
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ArXiv ePrint: 1904.07502
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Aharony, O., Urbach, E.Y. & Weiss, M. Generalized Hawking-Page transitions. J. High Energ. Phys. 2019, 18 (2019). https://doi.org/10.1007/JHEP08(2019)018
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DOI: https://doi.org/10.1007/JHEP08(2019)018