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Phase transitions in 3D gravity and fractal dimension

Dong, Xi and Maguire, Shaun and Maloney, Alexander and Maxfield, Henry (2018) Phase transitions in 3D gravity and fractal dimension. Journal of High Energy Physics, 2018 (5). Art. No. 80. ISSN 1126-6708. doi:10.1007/JHEP05(2018)080.

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We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS3 handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS3, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.

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Additional Information:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: March 19, 2018. Accepted: April 18, 2018. Published: May 14, 2018. Article funded by SCOAP3. We are very grateful to A. Belin, C. Keller and I. Zadeh for useful conversations. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN/00032-2015. This work was supported in part by a grant from the Simons Foundation (385602, A.M.). This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)SAPIN/00032-2015
Simons Foundation385602
Subject Keywords:AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory
Issue or Number:5
Record Number:CaltechAUTHORS:20180606-103432482
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Official Citation:Dong, X., Maguire, S., Maloney, A. et al. J. High Energ. Phys. (2018) 2018: 80.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86831
Deposited By: George Porter
Deposited On:06 Jun 2018 17:48
Last Modified:15 Nov 2021 20:42

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