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Dispersive CFT Sum Rules

Caron-Huot, Simon and Mazac, Dalimil and Rastelli, Leonardo and Simmons-Duffin, David (2020) Dispersive CFT Sum Rules. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20201118-074154634

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Abstract

We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule dispersive if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over Polyakov-Regge blocks. Unlike the usual OPE sum, the Polyakov-Regge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are non-negative above the double-twist gap; they have the physical interpretation of a subtracted version of superconvergence sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around mean-field theory, and to constrain the low-energy description of holographic CFTs with a large gap. We give examples of the first kind of applications, notably, we exhibit a candidate extremal functional for the spin-two gap problem.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2008.04931arXivDiscussion Paper
ORCID:
AuthorORCID
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:It is a pleasure to thank David Meltzer, Eric Perlmutter, Anh-Khoi Trinh, Sasha Zhiboedov, and Xinan Zhou for useful conversations. The work of D.M. and L.R. is supported in part by NSF grant # PHY-1915093. The work of S.C.-H. is supported by the National Science and Engineering Council of Canada, the Canada Research Chair program, the Fonds de Recherche du Québec - Nature et Technologies, and the Simons Collaboration on the Nonperturbative Bootstrap. D.S.-D. is supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap), a Sloan Research Fellowship, and a DOE Early Career Award under grant no. DE-SC0019085. Some of the computations in this work were performed on the Caltech High-Performance Cluster, partially supported by a grant from the Gordon and Betty Moore Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-1915093
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Canada Research Chairs ProgramUNSPECIFIED
Fonds de recherche du Québec - Nature et technologies (FRQNT)UNSPECIFIED
Simons Foundation488657
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0019085
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:Conformal field theory, dispersion relations, conformal bootstrap
Record Number:CaltechAUTHORS:20201118-074154634
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201118-074154634
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106716
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Nov 2020 18:38
Last Modified:18 Nov 2020 18:38

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