Breaking conformal invariance- Large N Chern-Simons theory coupled to massive fundamental fermions

TL;DR

This paper studies massive fermions coupled to a U(N) Chern-Simons gauge theory at large N and K, deriving exact propagators, partition functions, and analyzing high spin currents, revealing non-confining behavior despite broken conformal invariance.

Contribution

It provides exact solutions for fermion propagators and partition functions in large N, K limits, and demonstrates the persistence of high spin currents with mass, breaking conformal invariance.

Findings

Existence of infinite classically conserved high spin currents with mass.

Exact fermion propagator and partition function at finite temperature.

No confining spectrum in the three-dimensional Chern-Simons theory.

Abstract

We analyze the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory at level K. It is done in the large N, large K limits where \lambda=N/K is kept fixed. Following arXiv:1110.4386 we obtain the solution of a Schwinger-Dyson equation for the two point function, the exact expression for the fermion propagator and the partition function at finite temperature. We prove that in the large K limit there exists an infinite set of classically conserved high spin currents also when a mass is introduced, breaking the conformal invariance. In analogy to the seminal work of 't Hooft on two dimensional QCD, we write down a Bethe-Salpeter equation for the wave function of a "quark anti-quark" bound state. We show that unlike the two dimensional QCD case, the three dimensional Chern-Simons theory does not admit a confining spectrum.