Classifying GNY-like models

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.