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Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ

Collier, Scott and Kravchuk, Petr and Lin, Ying-Hsuan and Yin, Xi (2018) Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ. Journal of High Energy Physics, 2018 (9). Art. No. 150. ISSN 1126-6708. doi:10.1007/JHEP09(2018)150.

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We introduce spectral functions that capture the distribution of OPE coefficients and density of states in two-dimensional conformal field theories, and show that nontrivial upper and lower bounds on the spectral function can be obtained from semidefinite programming. We find substantial numerical evidence indicating that OPEs involving only scalar Virasoro primaries in a c > 1 CFT are necessarily governed by the structure constants of Liouville theory. Combining this with analytic results in modular bootstrap, we conjecture that Liouville theory is the unique unitary c > 1 CFT whose primaries have bounded spins. We also use the spectral function method to study modular constraints on CFT spectra, and discuss some implications of our results on CFTs of large c and large gap, in particular, to what extent the BTZ spectral density is universal.

Item Type:Article
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Kravchuk, Petr0000-0003-0977-3686
Additional Information:© The Author(s) 2018. 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: February 14, 2018; Revised: June 10, 2018; Accepted: September 23, 2018; Published: September 26, 2018. We are grateful to Daniel Harlow, Zohar Komargodski, David Simmons-Duffin, and Balt van Rees for discussions. PK, YL, and XY would like to thank the Center for Quantum Mathematics and Physics at University of California, Davis, PK and XY thank University of Kentucky, PK thanks Harvard University, XY thanks Korea Institute for Advanced Study, Stony Brook University, Indian String Meeting 2016, and Weizmann Institute, for their hospitality during the course of this work. This work is supported by a Simons Investigator Award from the Simons Foundation, by DOE grant DE-FG02-91ER40654, and by DOE grant DE-SC0011632 (PK, YL). SC is supported in part by the Natural Sciences and Engineering Research Council of Canada via a PGS D fellowship. YL is supported in part by the Sherman Fairchild Foundation. The numerical computations in this work are performed using the SDPB package [32] on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-FG02-91ER40654
Department of Energy (DOE)DE-SC0011632
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:Conformal and W Symmetry; Conformal Field Theory; Field Theories in Lower Dimensions; AdS-CFT Correspondence
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Issue or Number:9
Record Number:CaltechAUTHORS:20170209-151106792
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Official Citation:Collier, S., Kravchuk, P., Lin, YH. et al. J. High Energ. Phys. (2018) 2018: 150.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74200
Deposited By: Joy Painter
Deposited On:09 Feb 2017 23:42
Last Modified:11 Nov 2021 05:25

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