On-shell methods in quantum chromodynamics, supersymmetric Yang-Mills, and supergravity

By applying on-shell recursion relations, the scattering amplitudes for a pair of massive quarks and up to four gluons are presented. We write a formula for the spinors of the on-shell particle propagating between recursion diagrams. Auxiliary recursion relations allow us to prove that perturbative gravity amplitudes are well behaved under large complex deformations of the momenta of a pair of like-helicity gravitons. This establishes that on-shell recursion relations can be constructed for gravity amplitudes using these shifts. By applying the known expressions for SYM and SUGRA tree amplitudes, we write generating functions for the NNMHV box coefficients of SYM as well as the MHV, NMHV, and NN-MHV box coefficients for SUGRA. In support of the relation between dual Wilson loops and SYM scattering amplitudes at weak coupling, the SYM amplitudes are presented in a manifestly dual superconformal form. We introduce ordered box coefficients for efficiently calculating SUGRA quadruple cuts.