Coplanarity In Twistor Space Of N=4 Next-To-MHV One-Loop Amplitude Coefficients

TL;DR

This paper proves that the coefficients of next-to-MHV one-loop amplitudes in N=4 gauge theory are localized on a plane in twistor space, using differential operators on unitarity cuts.

Contribution

It demonstrates the coplanarity of amplitude coefficients in twistor space, providing a geometric understanding of their localization.

Findings

Coefficients are localized on a plane in twistor space.

Differential operators confirm coplanarity.

Provides a geometric interpretation of amplitude structure.

Abstract

Next-to-MHV one-loop amplitudes in N=4 gauge theory can be written as a linear combination of known multivalued functions, called scalar box functions, with coefficients that are rational functions. We consider the localization of these coefficients in twistor space and prove that all of them are localized on a plane. The proof is done by studying the action of differential operators that test coplanarity on the unitarity cuts of the amplitudes.