Classifying GNY-like models

TL;DR

This paper systematically classifies (2+1)d GNY-like models with scalar and fermion fields, identifies their fixed points in the epsilon expansion, and discovers a new fixed point called the 'orthogonal Heisenberg' CFT.

Contribution

It provides a comprehensive classification of GNY-like models and uncovers a novel fixed point, expanding the understanding of conformal field theories in 3D.

Findings

Identification of multiple fixed points in GNY-like models

Discovery of a new 'orthogonal Heisenberg' fixed point for M=3

Insights for conformal bootstrap studies

Abstract

We perform a systematic classification of (2+1)d Gross--Neveu--Yukawa-like models built out of one or more 4-component Dirac fermions and $M$ scalar fields, which preserve an O($M$) symmetry rotating the scalars. We then identify the perturbative fixed points of these models in the $4-\epsilon$ expansion. Our classification highlights several targets for the conformal bootstrap and reveals a new fixed point with $M=3$, which we call the "orthogonal Heisenberg" CFT.