Chern-Simons theory coupled to bifundamental scalars

TL;DR

This paper investigates a three-dimensional Chern-Simons theory with bifundamental scalars, revealing a line of fixed points at various ratios of gauge group ranks and analyzing the mass gap behavior on a torus.

Contribution

It demonstrates the existence of a line of fixed points at any M/N ratio and analyzes the mass gap for the theory on a torus at small M/N.

Findings

Existence of a line of fixed points at any M/N ratio.

Finite M/N gaps out light states on a torus.

Analysis of higher genus cases commented on.

Abstract

We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the $SU(N)_k \times SU(M)_{-k}$ gauge group. At small but fixed $M \ll N$, 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 $AdS_4$. 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.