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Reflections on Conformal Spectra

Kim, Hyungrok and Kravchuk, Petr and Ooguri, Hirosi (2016) Reflections on Conformal Spectra. Journal of High Energy Physics, 2016 (4). Art. No. 184. ISSN 1126-6708. doi:10.1007/JHEP04(2016)184.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Kravchuk, Petr0000-0003-0977-3686
Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: March 20, 2016; Accepted: April 11, 2016; Published: April 29, 2016. We thank S. El-Showk, N. Hunter-Jones, C. Keller, Z. Komargodski, Y. Nakayama, S. Rychkov, D. Simmons-Duffin, B. Stoica, and W. Yan for discussion. We also thank S. Rychkov and D. Simmons-Duffin for their comments on the draft of this paper. This work is supported in part by U.S. DOE grant DE-SC0011632, by the WPI Initiative of MEXT, by JSPS KAKENHI Grant Numbers C-26400240 and 15H05895, by the Simons Investigator Award, and by the Walter Burke Institute for Theoretical Physics and the Moore Center for Theoretical Cosmology and Physics at Caltech. We thank the hospitality of the Institute for Advanced Study, where HO is Director’s Visiting Professor. HO also thanks the Aspen Center for Physics and the Simons Center for Geometry and Physics, where parts of this work were done.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Japan Society for the Promotion of Science (JSPS)C-26400240
Japan Society for the Promotion of Science (JSPS)15H05895
Simons FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Conformal and W Symmetry; Field Theories in Higher Dimensions
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Issue or Number:4
Record Number:CaltechAUTHORS:20151104-124350087
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Official Citation:Kim, H., Kravchuk, P. & Ooguri, H. J. High Energ. Phys. (2016) 2016: 184.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61836
Deposited By: Joy Painter
Deposited On:04 Nov 2015 21:06
Last Modified:10 Nov 2021 22:54

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