Classifying GNY-like models

A bstract 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 – ϵ 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.