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Harmonic Analysis and Mean Field Theory

Karateev, Denis and Kravchuk, Petr and Simmons-Duffin, David (2019) Harmonic Analysis and Mean Field Theory. Journal of High Energy Physics, 2019 (10). Art. No. 217. ISSN 1126-6708. doi:10.1007/JHEP10(2019)217.

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We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and “seed” operators in 4d, and MFT for currents and stress-tensors in 3d.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Karateev, Denis0000-0003-4319-9681
Kravchuk, Petr0000-0003-0977-3686
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2019 The Authors. 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: August 2, 2019; Accepted: October 7, 2019; Published: October 21, 2019. We thank Murat Koloğlu, Eric Perlmutter and Matt Walters for discussions. DSD and PK are 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. PK is supported by DOE grant No. DE-SC0009988. DK is supported by Simons Foundation grant 488649 (Simons Collaboration on the Nonperturbative Bootstrap) and by the National Centre of Competence in Research Swiss MAP funded by the Swiss National Science Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0019085
Department of Energy (DOE)DE-SC0009988
Simons Foundation488649
Swiss National Science Foundation (SNSF)UNSPECIFIED
Subject Keywords:Conformal and W Symmetry; Conformal Field Theory
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Issue or Number:10
Record Number:CaltechAUTHORS:20180917-095421287
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89674
Deposited By: Joy Painter
Deposited On:17 Sep 2018 17:37
Last Modified:16 Nov 2021 00:37

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