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Title: Reflections on conformal spectra

Abstract

Here, we use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ0 as well as for large Δ0. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.

Authors:
 [1];  [1];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States); Institute for Advanced Study, Princeton, NJ (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States); Institute for Advanced Study, Princeton, NJ (United States); Univ. of Tokyo, Kashiwa (Tokyo)
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1435771
Grant/Contract Number:  
SC0011632
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: 2016; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Field Theories in Higher Dimensions

Citation Formats

Kim, Hyungrok, Kravchuk, Petr, and Ooguri, Hirosi. Reflections on conformal spectra. United States: N. p., 2016. Web. doi:10.1007/JHEP04(2016)184.
Kim, Hyungrok, Kravchuk, Petr, & Ooguri, Hirosi. Reflections on conformal spectra. United States. doi:10.1007/JHEP04(2016)184.
Kim, Hyungrok, Kravchuk, Petr, and Ooguri, Hirosi. Fri . "Reflections on conformal spectra". United States. doi:10.1007/JHEP04(2016)184. https://www.osti.gov/servlets/purl/1435771.
@article{osti_1435771,
title = {Reflections on conformal spectra},
author = {Kim, Hyungrok and Kravchuk, Petr and Ooguri, Hirosi},
abstractNote = {Here, we use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ0 as well as for large Δ0. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.},
doi = {10.1007/JHEP04(2016)184},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2016,
place = {United States},
year = {2016},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 14 works
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Figures / Tables:

Figure 1 Figure 1: Allowed range for Δx as a function of x for δ0 = 1 and δ0 = 1/2.

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Works referenced in this record:

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.