Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry

We investigate a class of relativistic fermion theories in 2<d<4 space-time dimensions with continuous chiral U(Nf)xU(Nf) symmetry. This includes a number of well-studied models, e.g., of Gross-Neveu and Thirring type, in a unified framework. Within the limit of pointlike interactions, the RG flow of couplings reveals a network of interacting fixed points, each of which defines a universality class. A subset of fixed points are "critical fixed points" with one RG relevant direction being candidates for critical points of second-order phase transitions. Identifying invariant hyperplanes of the RG flow and classifying their attractive/repulsive properties, we find evidence for emergent higher chiral symmetries as a function of Nf. For the case of the Thirring model, we discover a new critical flavor number that separates the RG stable large-Nf regime from an intermediate-Nf regime in which symmetry-breaking perturbations become RG relevant. This new critical flavor number has to be distinguished from the chiral-critical flavor number, below which the Thirring model is expected to allow spontaneous chiral symmetry breaking, and its existence offers a resolution to the discrepancy between previous results obtained in the continuum and the lattice Thirring models. Moreover, we find indications for a new feature of universality: details of the critical behavior can depend on additional "spectator symmetries" that remain intact across the phase transition. Implications for the physics of interacting fermions on the honeycomb lattice, for which our theory space provides a simple model, are given.