Topology of critical points and Hawking-Page transition

TL;DR

This paper investigates the topological properties of the Hawking-Page transition in AdS black holes using off-shell free energy constructions, revealing the topological charges of different phases and their relation to boundary gauge theories.

Contribution

It introduces a novel topological analysis of the Hawking-Page transition using off-shell free energy, linking bulk and boundary descriptions.

Findings

Topological charge of the transition point computed in bulk and boundary matches.

Stable and unstable phases have opposite topological charges.

Total topological charge of the system sums to zero.

Abstract

Using the Bragg-Williams construction of an off-shell free energy we compute the topological charge of the Hawking-Page transition point for black holes in AdS. A computation following from a related off-shell effective potential in the boundary gauge dual matches the value of topological charge obtained in the bulk. We also compute the topological charges of the equilibrium phases of these systems, which follow from the saddle points of the appropriate free energy. The locally stable and unstable phases turn out to have topological charges opposite to each other, with the total being zero, in agreement with the result obtained from a related construction [arXiv:2208.01932].