Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$

Abstract

We study $\mathcal{N}=3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the 't Hooft large $N$ limit, we compute the exact $2\to 2$ scattering amplitudes of the fundamental scalar superfields to all orders in the 't Hooft coupling $\lambda$. Our computations are presented in $\mathcal{N}=1$ superspace and make significant use of the residual $SO(2{)}_R$ symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact $2\to 2$ scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $\mathcal{N}=3$ theory in the planar limit is tree-level exact to all orders in the 't Hooft coupling $\lambda$. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.

v2: Minor changes