Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop

TL;DR

This paper develops generating functions for supersymmetric Yang-Mills and supergravity one-loop amplitudes, utilizing covariant superspace and ordered box coefficients, advancing the understanding of amplitude structures and dualities.

Contribution

It introduces all-multiplicity generating functions for NNMHV SYM and SUGRA box coefficients using covariant superspace and ordered coefficients, linking amplitude calculations with dual Wilson loops.

Findings

Generated all-multiplicity box coefficients for SYM and SUGRA.

Proved ordered coefficients produce physical amplitudes after permutations.

Verified results against existing literature.

Abstract

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.