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

TL;DR

This paper explores tensorial Gross-Neveu models in three dimensions, revealing new ultraviolet fixed points with reduced symmetry and a novel phase featuring spontaneous symmetry breaking.

Contribution

It introduces tensorial interactions to the Gross-Neveu model, uncovering new fixed points and phases not present in the standard model.

Findings

Existence of new ultraviolet fixed points with reduced symmetry.

Discovery of a phase with spontaneous symmetry breaking.

Phase diagram featuring a novel symmetry-breaking phase.

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.