Detachable circles and temperature-inversion dualities for CFT d

We use a Weyl transformation between S ¹ × S ^d-1 and {S}^1× H^{d-1}/Z to relate a conformal field theory at arbitrary temperature on S ^d-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 S ^d-1.