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Title: Universal spectrum of 2d conformal field theory in the large c limit

Abstract

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all \( \Delta \ge \frac{c}{6} \). The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

Authors:
 [1];  [2];  [3]
  1. Univ. of California, Santa Barbara, CA (United States)
  2. Rutgers Univ., Piscataway, NJ (United States)
  3. California Institute of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States); Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF)
OSTI Identifier:
1600491
Grant/Contract Number:  
SC0011632; SC0010008; SC0003883; SC0007897; PHY11-25915
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2014; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Lower Dimensions; AdS-CFT Correspondence

Citation Formats

Hartman, Thomas, Keller, Christoph A., and Stoica, Bogdan. Universal spectrum of 2d conformal field theory in the large c limit. United States: N. p., 2014. Web. doi:10.1007/JHEP09(2014)118.
Hartman, Thomas, Keller, Christoph A., & Stoica, Bogdan. Universal spectrum of 2d conformal field theory in the large c limit. United States. doi:10.1007/JHEP09(2014)118.
Hartman, Thomas, Keller, Christoph A., and Stoica, Bogdan. Mon . "Universal spectrum of 2d conformal field theory in the large c limit". United States. doi:10.1007/JHEP09(2014)118. https://www.osti.gov/servlets/purl/1600491.
@article{osti_1600491,
title = {Universal spectrum of 2d conformal field theory in the large c limit},
author = {Hartman, Thomas and Keller, Christoph A. and Stoica, Bogdan},
abstractNote = {Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all \( \Delta \ge \frac{c}{6} \). The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.},
doi = {10.1007/JHEP09(2014)118},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 9,
volume = 2014,
place = {United States},
year = {2014},
month = {9}
}

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    Cardy-like asymptotics of the 4d N = 4 $$ \mathcal{N}=4 $$ index and AdS5 blackholes
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    De Sitter holography and entanglement entropy
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