Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes

TL;DR

This paper develops geometric and twistor space interpretations for subleading color one-loop amplitudes in N=4 SYM, extending understanding of their structure and relations to leading color amplitudes, with detailed analysis for 5- and 6-point cases.

Contribution

It introduces a novel polytope interpretation for subleading amplitudes and a momentum twistor space representation for general N^kMHV amplitudes, building on relations to leading color amplitudes.

Findings

Polytope interpretation for subleading amplitudes in MHV case

Momentum twistor space representation for N^kMHV case

Detailed analysis of 5- and 6-point amplitudes

Abstract

We use the relation of the one-loop subleading-color amplitudes to the one-loop $n$-point leading color amplitudes in ${\cal N}=4$ SYM, to derive a polytope interpretation for the former in the $MHV$ case, and a representation in momentum twistor space for the general $N^kMHV$ case. These techniques are explored in detail for the 5-point and 6-point amplitudes. We briefly discuss the implications for IR divergences.