Chern–Simons theory with vector fermion matter

Abstract

We study three-dimensional conformal field theories described by U(N) Chern–Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger–Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on ℝ2 as a function of the ’t Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |λ|=1; the conformal theory does not exist for |λ|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N.