Detachable circles and temperature-inversion dualities for CFTd

Abstract

We use a Weyl transformation between S1 × Sd−1 and S1× ℋ d−1/ ℤ to relate a conformal field theory at arbitrary temperature on Sd−1 to itself at the inverse temperature on ℋ d−1/ 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 Sd−1.