On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit

TL;DR

This paper calculates the higher spin spectrum of a Chern-Simons theory coupled to fermions in the large flavor limit, revealing how anomalous dimensions behave at strong coupling and large spin, relevant for higher-spin holography.

Contribution

It provides the first detailed computation of higher spin current anomalous dimensions in this specific non-supersymmetric Chern-Simons-fermion theory at large N and M.

Findings

Anomalous dimensions reach a finite value at strong coupling.

Anomalous dimensions grow logarithmically with spin at large s.

The theory exhibits a slightly broken higher spin symmetry.

Abstract

In this note, we compute the higher spin spectrum of $U(M)_k$ Chern-Simons theory coupled to $N$ flavours of fundamental fermions, in the limit $N\gg M$ with the 't Hooft coupling $\lambda_M =\frac{N}{k_m}$ held fixed, to order $M/N$. This theory possesses a slightly broken higher spin symmetry, and may be of interest from the perspective of higher-spin and non-supersymmetric holography. We find that anomalous dimensions of the higher spin currents achieve a finite value at strong coupling $\lambda_M \rightarrow \infty$, which grows with spin as $\log s$ for large $s$, as expected for gauge theories.