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

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.

arXiv comment18 pages, 6 figures; corrected shift in quark bare mass parameter, clarified discussion of the fermion gap equation, various typos, appendix added

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