Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions

TL;DR

This paper investigates scattering amplitudes in three-dimensional N=2 supersymmetric gauge theories, deriving supersymmetry algebras, computing tree-level amplitudes, and proposing a BCFW recursion relation for mass-deformed theories.

Contribution

It provides the first derivation of on-shell supersymmetry algebras and computes explicit 3 and 4-point amplitudes in mass-deformed N=2 theories, introducing a BCFW recursion approach.

Findings

Odd-point amplitudes vanish in mass-deformed Chern-Simons theory.

All 4-point amplitudes can be expressed via superamplitudes.

Proposed BCFW recursion relation for mass-deformed 3D N=2 theories.

Abstract

We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with N=2 supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a BCFW recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed N=2 theories.