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Phase transitions in 3D gravity and fractal dimension

  • Xi Dong
  • Shaun Maguire
  • Alexander Maloney
  • Henry Maxfield
Open Access
Regular Article - Theoretical Physics
  • 64 Downloads

Abstract

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.

Keywords

AdS-CFT Correspondence Conformal and W Symmetry Conformal Field Theory 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Xi Dong
    • 1
  • Shaun Maguire
    • 2
  • Alexander Maloney
    • 3
  • Henry Maxfield
    • 3
  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Institute for Quantum Information & MatterCalifornia Institute for TechnologyPasadenaU.S.A.
  3. 3.Department of PhysicsMcGill UniversityMontréalCanada

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