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

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