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

TL;DR

This paper develops a formalism to compute and demonstrate the SO(N) invariance of S-matrices in three-dimensional N=2,4,8 SYM theories, linking on-shell amplitudes with superconformal Chern-Simons theories.

Contribution

It introduces a generalized spinor-helicity formalism for 3D SYM, proving SO(N) invariance of S-matrices and establishing a connection with M2-brane theories.

Findings

Manifest SO(N) invariance of four-particle amplitudes in N=2,4,8 SYM.

Recursion relations for tree amplitudes derived from 4D counterparts.

Explicit verification of four-particle amplitude calculations.

Abstract

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. Recursion relations relating tree amplitudes of three-dimensional SYM theories are shown to follow from their four-dimensional counterparts. The results for the four-particle amplitudes are verified by tree-level perturbative computations and a unitarity based construction of the integrand corresponding to the leading perturbative correction is also presented for the N=8 theory. For N=8 SYM, the manifest SO(8) symmetry is used to develop a map between the color-ordered amplitudes of the SYM and superconformal Chern-Simons theories, providing a direct connection between on-shell observables of D2 and M2-brane theories.