Tensorial Gross-Neveu models

We define and study various tensorial generalizations of the Gross-Neveu model in two dimensions, that is, models with four-fermion interactions and G3 symmetry, where we take either G = U(N) or G = O(N). Such models can also be viewed as two-dimensional generalizations of the Sachdev-Ye-Kitaev model, or more precisely of its tensorial counterpart introduced by Klebanov and Tarnopolsky, which is in part our motivation for studying them. Using the Schwinger-Dyson equations at large-N, we discuss the phenomenon of dynamical mass generation and possible combinations of couplings to avoid it. For the case G = U(N),we introduce an intermediate field representation and perform a stability analysis of the vacua. It turns out that the only apparently viable combination of couplings that avoids mass generation corresponds to an unstable vacuum. The stable vacuum breaks U(N)3 invariance, in contradiction with the Coleman-Mermin-Wagner theorem, but this is an artifact of the large-N expansion, similar to the breaking of continuous chiral symmetry in the chiral Gross-Neveu model.