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 $SU(N{)}_k\times SU(M{)}_{-k}$ 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 $Ad{S}_4$. 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.

1+27 pages, 6 figures; v2 has additional comments and a calculation in section 2 is corrected, all conclusions remain as before

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Cited by in corpus (11)

• Higher Spins & Strings
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Chern Simons Bosonization along RG Flows
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Chern-Simons-Ghost Theories and de Sitter Space
• Emergent gravity from Eguchi-Kawai reduction
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Emergent Supersymmetry at Large $N$
• Three Dimensional Bosonization From Supersymmetry