Detachable circles and temperature-inversion dualities for CFT$_d$

TL;DR

This paper explores a Weyl transformation linking finite-temperature conformal field theories on different geometries, revealing phase transitions, dualities, and new bulk solutions in gauge/gravity duality.

Contribution

It introduces a novel temperature-inversion duality for CFTs on spheres and hyperbolic spaces, with implications for phase transitions and holographic duals.

Findings

Identifies a confining phase transition at finite temperature.

Constructs smooth bulk solutions with conical singularities at the boundary.

Establishes a high-temperature/low-temperature duality for CFTs on spheres.

Abstract

We use a Weyl transformation between $S^1 \times S^{d-1}$ and $S^1 \times \mathcal{H}^{d-1}/\mathbb{Z}$ to relate a conformal field theory at arbitrary temperature on $S^{d-1}$ to itself at the inverse temperature on $\mathcal{H}^{d-1}/\mathbb{Z}$. We use this equivalence to deduce a confining phase transition at finite temperature for large-$N$ gauge theories on hyperbolic space. In the context of gauge/gravity duality, this equivalence provides new examples of smooth bulk solutions which asymptote to conically singular geometries at the AdS boundary. We also discuss implications for the Eguchi-Kawai mechanism and a high-temperature/low-temperature duality on $S^{d-1}$.