Chern-Simons theory coupled to bifundamental scalars

We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the $SU(N)k \times SU(M){-k}$gaugegroup\mathrm{.}Atsmallbutfixed$M \ll N$, 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 $Ad{S}_4$. At finite $M\mathrm{/}N$ 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 $M\mathrm{/}N$. We also prove that turning on a finite but small $M\mathrm{/}N$ 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.