Published October 2019
| Submitted + Published
Journal Article
Open
Harmonic Analysis and Mean Field Theory
Chicago
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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
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Additional details
- Eprint ID
- 89674
- Resolver ID
- CaltechAUTHORS:20180917-095421287
- 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
- Created
-
2018-09-17Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2018-036