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On the higher spin spectrum of Chern-Simons theory coupled to fermions in the large flavour limit. (English) Zbl 1387.58028

Summary: 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.

MSC:

58J28 Eta-invariants, Chern-Simons invariants
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

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