Chern-Simons Theory with Vector Fermion Matter

TL;DR

This paper analyzes a three-dimensional conformal field theory involving Chern-Simons gauge fields coupled to massless fermions, computing exact free energy, operator spectra, and correlators, revealing a rich higher spin symmetry structure and a critical coupling limit.

Contribution

It provides the first exact calculation of the free energy at finite temperature and explores the operator spectrum and correlators, establishing connections to higher spin algebras and string theory limits.

Findings

Free energy vanishes at |lambda|=1, indicating a non-existence of the conformal theory beyond this point.

Higher spin currents do not acquire anomalous dimensions at leading order in 1/N.

Explicit perturbative results for three-point functions up to two loops.

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 lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R^2 as a function of the 't Hooft coupling lambda=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |lambda|=1; the conformal theory does not exist for |lambda|>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. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W-infinity algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.