Chern-Simons theory coupled to bifundamental scalars

Abstract

We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the SU(N) k × SU(M)-k gauge group. At small but fixed M ≪ N, this system approaches the theory of a Chern-Simons field coupled to fundamental matter, conjectured to be dual to a parity-violating version of Vasiliev's higher-spin gauge theory in AdS4. At finite M/N and large 't Hooft coupling this theory (or its SUSY version) is expected to be dual to an Einstein-like gravity. We show at two loops that this theory possesses a line of fixed points at any value of M/N. We also prove that turning on a finite but small M/N gaps out the light states that Chern-Simons theory coupled to fundamental matter develops when placed on a torus. We also comment on the higher genus case. © 2014 The Author(s).