Dr Abhishek Agarwal (American Physical Society)
An on-shell formalism for the computation of S-matrices of SYM theories in three spacetime dimensions will be presented. The framework is a generalization of the spinor-helicity formalism in four dimensions. The formalism will be 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 will be used to argue for the SO(N) invariance of the S-matrices of these theories: a claim which will be proved explicitly for the four-particle scattering amplitudes. Recursion relations relating tree amplitudes of three-dimensional SYM theories will be shown to follow from their four-dimensional counterparts. The results for the four-particle amplitudes will be shown to be verified by tree-level perturbative computations and a unitarity based construction of the integrand corresponding to the leading perturbative correction will also be presented for the N=8 theory. For N=8 SYM, the manifest SO(8) symmetry will be 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.