Harmonic Analysis and Mean Field Theory
High Energy Physics - Theory
2020-01-08 v1
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.
Cite
@article{arxiv.1809.05111,
title = {Harmonic Analysis and Mean Field Theory},
author = {Denis Karateev and Petr Kravchuk and David Simmons-Duffin},
journal= {arXiv preprint arXiv:1809.05111},
year = {2020}
}
Comments
58 pages + appendices