Deconstructing Supersymmetric S-matrices in D <= 2 + 1

TL;DR

This paper reveals the hidden supersymmetric structures of S-matrices in 3D Yang-Mills theories with various N supersymmetries, connecting them to Chern-Simons theories and discussing dimensional reduction.

Contribution

It identifies the specific supersymmetry groups of S-matrices in 3D N=2, 4, 8 theories and maps these to their representations in related Chern-Simons-Matter theories.

Findings

SU(1|1), SU(2|2), and SU(2|2) x SU(2|2) are the supersymmetries of the S-matrices.

A direct correspondence between these symmetries and Yang-Mills degrees of freedom is established.

Dimensional reduction to 2D observables is discussed.

Abstract

Global supersymmetries of the S-matrices of N = 2, 4, 8 supersymmetric Yang-Mills theories in three spacetime dimensions (without matter hypermultiplets) are shown to be SU(1|1), SU(2|2) and SU(2|2) X SU(2|2) respectively. These symmetries are not manifest in the off-shell Lagrangian formulations of these theories. A direct map between these symmetries and their representations in terms of the Yang-Mills degrees of freedom and the corresponding quantities in Chern-Simons-Matter theories with N >= 4 supersymmetry is also obtained. Dimensional reduction of the on-shell observables of the Yang-Mills theories to two spacetime dimensions is also discussed.