On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts

TL;DR

This paper introduces algebraic and diagrammatic methods to analyze supersymmetric sums in multi-loop unitarity cuts, focusing on maximally supersymmetric Yang-Mills amplitudes and their relation to supergravity.

Contribution

It presents new algebraic and diagrammatic techniques for evaluating supersymmetric sums in multi-loop amplitudes, extending to supergravity via KLT relations.

Findings

Methods simplify calculations of multi-loop amplitudes.

Concrete examples relevant for four-loop amplitude calculations.

Results applicable to supergravity amplitudes through established relations.

Abstract

In this paper we describe algebraic and diagrammatic methods, related to the MHV generating function method, for evaluating and exposing the structure of supersymmetric sums over the states crossing generalized unitarity cuts of multi-loop amplitudes in four dimensions. We focus mainly on cuts of maximally supersymmetric Yang-Mills amplitudes. We provide various concrete examples, some of which are directly relevant for the calculation of four-loop amplitudes. Additionally, we discuss some cases with less than maximal supersymmetry. The results of these constructions carry over to generalized cuts of multi-loop supergravity amplitudes through use of the Kawai-Lewellen-Tye relations between gravity and gauge-theory tree amplitudes.