Reflections on conformal spectra
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:

^{[1]};
^{[1]};
^{[2]}
 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:
 Grant/Contract Number:
 SC0011632
 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
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Field Theories in Higher Dimensions
 OSTI Identifier:
 1435771
Kim, Hyungrok, Kravchuk, Petr, and Ooguri, Hirosi. Reflections on conformal spectra. United States: N. p.,
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. 2016.
"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 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}
}