Hidden Local and Non-local Symmetries of S-matrices of N=2,4,8 SYM in D=2+1

TL;DR

This paper explores hidden symmetries in the tree-level S-matrices of three-dimensional N=2,4,8 super Yang-Mills theories, revealing algebraic structures and non-local symmetries using an on-shell formalism inspired by four-dimensional spinor-helicity methods.

Contribution

It introduces an on-shell formalism for 3D theories that uncovers hidden symmetries and algebraic structures in their scattering amplitudes, including a manifest SO(N) symmetry to all orders.

Findings

Manifest SO(N) symmetry of S-matrix to all orders

Identification of non-local symmetries in N=8 theory

Connection to D2-M2 brane dualities

Abstract

This talk, based principally on arXiv:1103.0786, is devoted to properties of tree-level S-matrices of N=2,4,8 SYM in D=2+1. We'll discuss an on-shell formalism for three-dimensional theories inspired by the spinor-helicity framework in four spacetime dimensions. Our framework will be shown be to particularly well suited for the extraction of hidden symmetries and algebraic structures that the scattering amplitudes of the three-dimensional theories posses. In particular we shall discuss the manifest SO(N) symmetry of the S-matrix to all orders in perturbation theory; a symmetry that the Lagrangians of these theories do not have. After a brief discussion of the ramification of the SO(N) invariance to the D2-M2 brane dualities, we shall introduce an on-shell superfield framework for three-dimensional theories and end with a surprising hint of the existence of non-local symmetries for the S-matrix of the N=8 theory.