Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions

Abstract

Perturbing the standard Gross-Neveu model for $N^3$ fermions by quartic interactions with the appropriate tensorial contraction patterns, we reduce the original $U(N^3)$ symmetry to either $U(N)\times U(N^2)$ or $U(N)\times U(N)\times U(N)$. In the large-$N$ limit, we show that in three dimensions such models admit new ultraviolet fixed points with reduced symmetry, besides the well-known one with maximal symmetry. The phase diagram notably presents a new phase with spontaneous symmetry breaking of one $U(N)$ component of the symmetry group.