Instability of Chern-Simons Theory with Fermions at Large N

TL;DR

This paper investigates the stability of the dynamical gap solution in large N Chern-Simons gauge theory with fermions, revealing saddle-point instabilities and comparing with QCD-like theories to understand scale symmetry breaking.

Contribution

It provides an analytical analysis of the saddle-point instability in Chern-Simons theory with fermions using auxiliary-field and CJT effective potentials, a novel approach in this context.

Findings

Identified saddle-point instability around the gap solution.

Compared stability features with QCD-like theories.

Enhanced understanding of scale symmetry breaking in the model.

Abstract

We study the (in)stability around the dynamical gap solution of the $U(N)$ Chern-Simons gauge theory with fundamental fermions (massless or massive) coupled in $D=3$ at large $N$. Explicit analyses on both the Auxiliary-Field (AF) and the Cornwall-Jackiw-Tomboulis (CJT) effective potentials are given. In both approaches we manage to analytically identify the saddle-point instability around the gap solution. We also give a comparison with the QCD-like theories. This study can help understanding the scale symmetry breaking picture of this theory.