Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2019)217
Keywords
Conformal and W Symmetry; Conformal Field Theory
Categories
Funding
- Simons Foundation [488649, 488657]
- Sloan Research Fellowship
- DOE [DE-SC0009988, DE-SC0019085]
- National Centre of Competence in Research SwissMAP - Swiss National Science Foundation
- U.S. Department of Energy (DOE) [DE-SC0019085] Funding Source: U.S. Department of Energy (DOE)
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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.
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