d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

TL;DR

This paper explores three-dimensional Chern-Simons theories coupled to scalar fields, revealing a family of conformal fixed points with higher-spin symmetry and suggesting a continuum of dual higher-spin gravity theories parameterized by the 't Hooft coupling.

Contribution

It introduces a parity-breaking deformation of vector models coupled to Chern-Simons gauge theories, analyzing their fixed points and operator spectra at large N and finite coupling.

Findings

Existence of a line of conformal fixed points parameterized by the 't Hooft coupling.

Spectrum of primary operators remains the same as the free theory at infinite N.

Correlation functions depend on the 't Hooft coupling, indicating a family of dual higher-spin theories.

Abstract

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.