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 fourpoint function in any dimension in the limit of large scaling dimensions Δ_{0} 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 fourpoint functions are valid for finite Δ_{0} as well as for large Δ_{0}. 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 fourpoint function.
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States); Institute for Advanced Study, Princeton, NJ (United States)
 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 Institute of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 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 10298479
 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. https://doi.org/10.1007/JHEP04(2016)184.
Kim, Hyungrok, Kravchuk, Petr, & Ooguri, Hirosi. Reflections on conformal spectra. United States. https://doi.org/10.1007/JHEP04(2016)184
Kim, Hyungrok, Kravchuk, Petr, and Ooguri, Hirosi. Fri .
"Reflections on conformal spectra". United States. https://doi.org/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 fourpoint 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 fourpoint 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 fourpoint 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}
}
Web of Science
Figures / Tables:
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Works referencing / citing this record:
The effective bootstrap
journal, September 2016
 Echeverri, Alejandro Castedo; von Harling, Benedict; Serone, Marco
 Journal of High Energy Physics, Vol. 2016, Issue 9
The conformal bootstrap: Theory, numerical techniques, and applications
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 Poland, David; Rychkov, Slava; Vichi, Alessandro
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Figures / Tables found in this record: