The Inversion Formula and 6j Symbol for 3d Fermions
Abstract
In this work we study the symbol of the conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning symbols to the simpler symbol for four scalar operators. As one application we use these techniques to compute mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.
Cite
@article{arxiv.2006.07374,
title = {The Inversion Formula and 6j Symbol for 3d Fermions},
author = {Soner Albayrak and David Meltzer and David Poland},
journal= {arXiv preprint arXiv:2006.07374},
year = {2020}
}
Comments
63 pages, 7 figures, 1 attached Mathematica notebook