A test of bosonization at the level of four-point functions in Chern-Simons vector models

Abstract

We study four-point functions in Chern-Simons vector models in the large $N$ limit. We compute the four-point function of the scalar primary to all orders in the `t Hooft coupling $\lambda =N/k$ in $U(N{)}_k$ Chern-Simons theory coupled to a fundamental fermion, in both the critical and non-critical theory, for a particular case of the external momenta. These theories cover the entire 3-parameter "quasi-boson" and 2-parameter "quasi-fermion" families of 3-dimensional quantum field theories with a slightly-broken higher spin symmetry. Our results are consistent with the celebrated bosonization duality, as we explicitly verify by calculating four-point functions in the free critical and non-critical bosonic theories.

20 pages, various improvements

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• Large N Renormalization Group Flows in 3d $\mathcal{N}=1$ Chern-Simons-Matter Theories
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
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• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
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• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
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