The Massive Fermion Phase for the U(N) Chern-Simons Gauge Theory in D=3 at Large N

TL;DR

This paper investigates the phase structure of large N fermions in U(N) Chern-Simons theory in three dimensions, revealing a massive phase with spontaneous scale symmetry breaking and Goldstone boson emergence.

Contribution

It provides an exact leading-order solution for the massive phase and demonstrates spontaneous scale symmetry breaking in the large N limit.

Findings

Existence of a massive phase with spontaneous scale symmetry breaking

Identification of the Goldstone boson associated with scale symmetry breaking

Evidence supporting the conformal behavior in the large N limit

Abstract

We explore the phase structure of fermions in the U(N) Chern-Simons gauge theory in three dimensions using the large N limit where N is the number of colors and the fermions are taken to be in the fundamental representation of the U(N) gauge group. In the large N limit, the theory retains its classical conformal behavior and considerable attention has been paid to a possible AdS/CFT duality of the theory in the conformal phase. In this paper we present a solution for the massive phase of the fermion theory that is exact to the leading order of 't Hooft's large N expansion. We present evidence for the spontaneous breaking of the exact scale symmetry and analyze the properties of the dilation that appears as the Goldstone boson of scale symmetry breaking.