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arXiv · 1709.06084

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

Gary T. Horowitz·Edgar Shaghoulian
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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 $S^{d-1}$.

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Gary T. Horowitz, Edgar Shaghoulian. 2017-09-18. Detachable circles and temperature-inversion dualities for CFT$_d$. https://doi.org/10.1007/jhep01(2018)135

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