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

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

20 pages, 8 figures, v2: added references

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• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Momentum space parity-odd CFT 3-point functions
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Chern-Simons dualities with multiple flavors at large $N$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• The Hilbert Space of large $N$ Chern-Simons matter theories
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Emergent Supersymmetry at Large $N$
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$