Large N planar or bare vertex approximation and critical behavior of a SU(N) invariant four-fermion model in 2+1 dimensions

TL;DR

This paper analytically solves a 2+1 dimensional SU(N) invariant four-fermion model in the large N limit, revealing its critical behavior and universality class, which differs from the Gross-Neveu model.

Contribution

It introduces an analytical solution for the critical behavior of a four-fermion model using the 1/N expansion and ladder approximation, highlighting its distinct universality class.

Findings

Critical coupling and exponents are derived as functions of N.

The model's universality class differs from the Gross-Neveu model.

Planar diagrams dominate in the large N limit, corresponding to the ladder approximation.

Abstract

A four-fermion model in 2+1 dimensions describing N Dirac fermions interacting via SU(N) invariant N^2-1 four-fermion interactions is solved in the leading order of the 1/N expansion. The 1/N expansion corresponds to 't Hoofts topological 1/N expansion in which planar Feynman diagrams prevail. For the symmetric phase of this model, it is argued that the planar expansion corresponds to the ladder approximation. A truncated set of Schwinger-Dyson equations for the fermion propagator and composite boson propagator representing the relevant planar diagrams is solved analytically. The critical four-fermion coupling and various critical exponents are determined as functions of N. The universality class of this model turns out to be quite distinct from the Gross-Neveu model in the large N limit.