CaltechAUTHORS
Published October 2019 | Version Submitted + Published
Journal Article Open

Harmonic Analysis and Mean Field Theory

Creators

  • 1. ROR icon École Polytechnique Fédérale de Lausanne
  • 2. ROR icon California Institute of Technology
  • 3. ROR icon Institute for Advanced Study

Abstract

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.

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.

Attached Files

Published - Karateev2019_Article_HarmonicAnalysisAndMeanFieldTh.pdf

Submitted - 1809.05111.pdf

Files

1809.05111.pdf

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Additional details

Identifiers

Eprint ID
89674
Resolver ID
CaltechAUTHORS:20180917-095421287

Related works

Describes
https://arxiv.org/abs/1809.05111 (URL)

Funding

Simons Foundation
488657
Alfred P. Sloan Foundation
Department of Energy (DOE)
DE-SC0019085
Department of Energy (DOE)
DE-SC0009988
Simons Foundation
488649
Swiss National Science Foundation (SNSF)
SCOAP3

Dates

Created
2018-09-17
Created from EPrint's datestamp field
Updated
2021-11-16
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Walter Burke Institute for Theoretical Physics , Physics Department
Other Numbering System Name
CALT-TH
Other Numbering System Identifier
2018-036