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

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 $S^{d-1}$.

21 pages

References in corpus (3)

• Towards a derivation of holographic entanglement entropy
• Holographic models of de Sitter QFTs
• A scalar field condensation instability of rotating anti-de Sitter black holes

Cited by in corpus (11)

• Global symmetry, Euclidean gravity, and the black hole information problem
• Universal Asymptotics for High Energy CFT Data
• Thermal Conformal Blocks
• Parity and the modular bootstrap
• Comments on a state-operator correspondence for the torus
• Flat space gravity at finite cutoff
• Deforming black holes in AdS
• Notes on massless scalar field partition functions, modular invariance and Eisenstein series
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Sparseness bounds on local operators in holographic $CF{T}_d$
• Modular properties of massive scalar partition functions