Scattering amplitudes in N $$ \mathcal{N} $$ = 3 supersymmetric SU(N) Chern-Simons-matter theory at large N

Abstract

Abstract We study N $$ \mathcal{N} $$ = 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 → 2 scattering amplitudes of the fundamental scalar superfields to all orders in the ’t Hooft coupling λ. Our computations are presented in N $$ \mathcal{N} $$ = 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 → 2 scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the N $$ \mathcal{N} $$ = 3 theory in the planar limit is tree-level exact to all orders in the ’t Hooft coupling λ. 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.

Keywords

• Chern-Simons Theories
• Scattering Amplitudes
• 1/N Expansion
• Supersym- metric Gauge Theory