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2019

Generalized Hawking-Page transitions

Aharony, Ofer, Urbach, Erez Y., Weiss, Maya

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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.

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Built on

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E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
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M. Henningson and K. Skenderis, The Holographic Weyl anomaly
1998
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E. Witten and S.-T. Yau, Connectedness of the boundary in the AdS / CFT correspondence
1999
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