  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 NNMHV box coefficients for SUGRA. The all-multiplicity generating
functions utilize covariant, on-shell superspace whereby the contribution from
arbitrary external states in the supermultiplet can be extracted by Grassmann
operators. 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
calculating SUGRA quadruple cuts and prove that ordered coefficients generate
physical cut amplitudes after summing over permutations of the external legs.
The ordered box coefficients are produced by sewing ordered subamplitudes,
previously used in applying on-shell recursion relations at tree level. We
describe our verification of the results against the literature, and a formula
for extracting the contributions from external gluons or gravitons to NNMHV
superamplitudes is presented.
