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:
-
- Univ. of California, Santa Barbara, CA (United States)
- Rutgers Univ., Piscataway, NJ (United States)
- 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); National Science Foundation (NSF)
- OSTI Identifier:
- 1600491
- Grant/Contract Number:
- SC0011632; SC0010008; SC0003883; SC0007897; PHY11-25915
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); 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. https://doi.org/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. https://doi.org/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)},
number = 9,
volume = 2014,
place = {United States},
year = {Mon Sep 22 00:00:00 EDT 2014},
month = {Mon Sep 22 00:00:00 EDT 2014}
}
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