Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM

Understand

An on-shell formalism for the computation of S-matrices of SYM theories in three spacetime dimensions is presented.

• The framework is a generalization of the spinor-helicity formalism in four dimensions.
• The formalism is applied to establish the manifest SO(N) covariance of the on-shell superalgebra relevant to N =2,4 and 8 SYM theories in d=3.
• The results are then used to argue for the SO(N) invariance of the S-matrices of these theories: a claim which is proved explicitly for the four-particle scattering amplitudes.