The Inversion Formula and 6j Symbol for 3d Fermions

Autor:	Albayrak, Soner, Meltzer, David, Poland, David
Rok vydání:	2020
Předmět:	High Energy Physics - Theory Condensed Matter - Statistical Mechanics Condensed Matter - Strongly Correlated Electrons High Energy Physics - Lattice Mathematical Physics
Zdroj:	JHEP 09 (2020) 148
Druh dokumentu:	Working Paper
DOI:	10.1007/JHEP09(2020)148
Popis:	In this work we study the $6j$ symbol of the $3d$ 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 $6j$ symbols to the simpler $6j$ symbol for four scalar operators. As one application we use these techniques to compute $3d$ 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. Comment: 63 pages, 7 figures, 1 attached Mathematica notebook
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.07374 Zobrazit plný text záznamu View this record from Arxiv