Tensorial Gross-Neveu models

Dario Benedetti (1) , Sylvain Carrozza , Razvan Gurau (2) , Alessandro Sfondrini

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 CPHT - Centre de Physique Théorique [Palaiseau]

We define and study various tensorial generalizations of the Gross-Neveu model in two dimensions, that is, models with four-fermion interactions and G$^{3}$ 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.

Mots clés: 1/N Expansion; Field Theories in Lower Dimensions; Nonperturbative Effects; Renormalization Group; dimension: 2; Gross-Neveu model: chiral; expansion 1/N; symmetry: chiral; vacuum state: stability; U(N); mass generation; four-fermion interaction; Dyson-Schwinger equation; O(N)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Dario Benedetti, Sylvain Carrozza, Razvan Gurau, Alessandro Sfondrini. Tensorial Gross-Neveu models. Journal of High Energy Physics, 2018, 01, pp.003. ⟨10.1007/JHEP01(2018)003⟩. ⟨hal-01704764⟩