Gauged Nambu-Jona-Lasinio Model at O(1/N) with and without a Chern-Simons Term

TL;DR

This paper analyzes the gauged Nambu-Jona-Lasinio model at large N, calculating critical exponents and exploring the effects of a Chern-Simons term on these exponents in three dimensions.

Contribution

It provides an exact large N solution of the model, including the impact of a Chern-Simons term on critical behavior and exponents.

Findings

Computed anomalous dimensions and critical exponents at leading order in 1/N.

Demonstrated the theta-dependence of critical exponents with a Chern-Simons term.

Extended analysis to three-dimensional models with topological term influence.

Abstract

We solve the gauged Nambu--Jona-Lasinio model at leading order in the large $N$ expansion by computing the anomalous dimensions of all the fields of the model and other gauge independent critical exponents by examining the scaling behaviour of the Schwinger Dyson equation. We then restrict to the three dimensional model and include a Chern Simons term to discover the $\theta$-dependence of the same exponents where $\theta$ is the Chern Simons coupling.