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Title: Poincaré series, 3D gravity and CFT spectroscopy

Abstract

Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have positive spectrum. This allows us to efficiently extract the constraints on the CFT spectrum imposed by modular invariance, giving information on the spectrum that goes beyond the Cardy growth of the asymptotic density of states. Some of the candidate modular invariant partition functions we construct have gaps of size (c - 1)/12, proving that gaps of this size and smaller are consistent with modular invariance. We also revisit the partition function of pure Einstein gravity in AdS3 obtained by summing over geometries, which has a spectrum with two unphysical features: it is continuous, and the density of states is not positive definite. We show that both of these can be resolved by adding corrections to the spectrum which are subleading in the semi-classical (large central charge) limit.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Rutgers Univ., Piscataway, NJ (United States)
  2. McGill Univ., Montreal, QC (Canada). Dept. of Physics; Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
Publication Date:
Research Org.:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1454524
Grant/Contract Number:  
SC0007897; SC0010008; SC0003883
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: 2015; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; conformal and W symmetry; field theories in lower dimensions

Citation Formats

Keller, Christoph A., and Maloney, Alexander. Poincaré series, 3D gravity and CFT spectroscopy. United States: N. p., 2015. Web. doi:10.1007/JHEP02(2015)080.
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Keller, Christoph A., & Maloney, Alexander. Poincaré series, 3D gravity and CFT spectroscopy. United States. https://doi.org/10.1007/JHEP02(2015)080
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Keller, Christoph A., and Maloney, Alexander. Thu . "Poincaré series, 3D gravity and CFT spectroscopy". United States. https://doi.org/10.1007/JHEP02(2015)080. https://www.osti.gov/servlets/purl/1454524.
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@article{osti_1454524,
title = {Poincaré series, 3D gravity and CFT spectroscopy},
author = {Keller, Christoph A. and Maloney, Alexander},
abstractNote = {Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have positive spectrum. This allows us to efficiently extract the constraints on the CFT spectrum imposed by modular invariance, giving information on the spectrum that goes beyond the Cardy growth of the asymptotic density of states. Some of the candidate modular invariant partition functions we construct have gaps of size (c - 1)/12, proving that gaps of this size and smaller are consistent with modular invariance. We also revisit the partition function of pure Einstein gravity in AdS3 obtained by summing over geometries, which has a spectrum with two unphysical features: it is continuous, and the density of states is not positive definite. We show that both of these can be resolved by adding corrections to the spectrum which are subleading in the semi-classical (large central charge) limit.},
doi = {10.1007/JHEP02(2015)080},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2015,
place = {United States},
year = {Thu Feb 12 00:00:00 EST 2015},
month = {Thu Feb 12 00:00:00 EST 2015}
}
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https://doi.org/10.1007/JHEP02(2015)080
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