Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes

TL;DR

This work investigates the twistor-space structure of box-function coefficients in $N=1$ one-loop amplitudes, focusing on six-point configurations and selective higher-point cases. Using basis-function decompositions, cut-constructibility, and twistor-operator tests, it shows that for next-to-MHV amplitudes, box coefficients have planar support in twistor space, mirroring known $N=4$ results, while configurations with more negative helicities do not preserve this property. The analysis extends to higher points, deriving general $D=6$ box-numerator forms and confirming the robustness of the planar twistor-space picture in $N=1$ theories. The results offer a geometric organizing principle that can constrain and guide the reconstruction of loop amplitudes in supersymmetric gauge theories.

Abstract

We examine the coefficients of the box functions in N=1 supersymmetric one-loop amplitudes. We present the box coefficients for all six point N=1 amplitudes and certain all $n$ example coefficients. We find for ``next-to MHV'' amplitudes that these box coefficients have coplanar support in twistor space.