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

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 $M\mathrm{/}N$. 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 ${\lambda }_M\to \mathrm{\infty }$, which grows with spin as $\log s$ for large $s$, as expected for gauge theories.