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 \(M/N\). 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.