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 → 2 scattering amplitudes of the fundamental scalar superfields to all orders in the ’t Hooft coupling λ. 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 → 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 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.
Highlights
Pure Chern-Simons theories in the absence of matter are topological and have no propagating degrees of freedom
We find that the scattering amplitude of the N = 3 theory in the planar limit is tree-level exact to all orders in the ’t Hooft coupling λ
Since the SO(2)R symmetry is a global symmetry of the action (2.12) in N = 1 superspace, it follows that the non-trivial S-matrices constructed in the N = 1 language have to be invariant under this symmetry, i.e. they have zero net SO(2)R charge
Summary
Pure Chern-Simons theories in the absence of matter are topological and have no propagating degrees of freedom. Chern-Simons-matter theories, the 2 → 2 scattering amplitude computed to all orders in the ’t Hooft coupling remains tree-level exact (vanishing loop corrections to all orders) [27]. Enjoy invariance under dual superconformal symmetry and Yangian symmetry [56, 57] While this is sufficient motivation for us to study the scattering amplitudes in supersymmetric Chern-Simons-matter theories, there is a significant technical roadblock as we go to higher supersymmetries. In particular we compute 2 → 2 scattering amplitudes in N = 3 supersymmetric SU(N ) Chern-Simons-matter theories coupled to fundamental matter at large. The special kinematic limit q± = 0 in which the correlation functions were computed allows direct extraction of the scattering amplitudes in the symmetric, anti-symmetric and adjoint channels. Some supplementary equations are given in appendix C, and appendix D is a summary of the tree level superamplitude in the theory
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