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. https://resolver.caltech.edu/CaltechAUTHORS:20180917-095421287

	PDF - Published Version Creative Commons Attribution. 1MB
	PDF - Submitted Version See Usage Policy. 890kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180917-095421287

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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/JHEP10(2019)217	DOI	Article
https://arxiv.org/abs/1809.05111	arXiv	Discussion Paper

ORCID:

Author	ORCID
Karateev, Denis	0000-0003-4319-9681
Kravchuk, Petr	0000-0003-0977-3686
Simmons-Duffin, David	0000-0002-2937-9515

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

Funders:

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

Subject Keywords:

Conformal and W Symmetry; Conformal Field Theory

Other Numbering System:

Other Numbering System Name	Other Numbering System ID
CALT-TH	2018-036

Issue or Number:

DOI:

10.1007/JHEP10(2019)217

Record Number:

CaltechAUTHORS:20180917-095421287

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20180917-095421287

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

89674

Collection:

CaltechAUTHORS

Deposited By:

Joy Painter

Deposited On:

17 Sep 2018 17:37

Last Modified:

16 Nov 2021 00:37

Repository Staff Only: item control page