3 years ago

# Detachable circles and temperature-inversion dualities for CFT d

Edgar Shaghoulian, Gary T. Horowitz

### Abstract

We use a Weyl transformation between S1 × Sd−1 and $${S}^1\times {\mathrm{\mathscr{H}}}^{d-1}/\mathbb{Z}$$ to relate a conformal field theory at arbitrary temperature on Sd−1 to itself at the inverse temperature on $${\mathrm{\mathscr{H}}}^{d-1}/\mathbb{Z}$$ . 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 Sd−1.

DOI: 10.1007/JHEP01(2018)135

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