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Harmonic Analysis and Mean Field Theory

Karateev, Denis and Kravchuk, Petr and Simmons-Duffin, David (2018) Harmonic Analysis and Mean Field Theory. . (Submitted)

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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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Kravchuk, Petr0000-0003-0977-3686
Simmons-Duffin, David0000-0002-2937-9515
Additional Information: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 SwissMAP funded by the Swiss National Science Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Department of Energy (DOE)DE-SC0019085
Department of Energy (DOE)DE-SC0009988
Alfred P. Sloan FoundationUNSPECIFIED
Simons Foundation488649
Swiss National Science Foundation (SNSF)UNSPECIFIED
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Other Numbering System NameOther Numbering System ID
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:17 Sep 2018 17:37

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