Twistor transform of all tree amplitudes in N=4 SYM theory

TL;DR

This paper explores the twistor transform of all tree-level superamplitudes in N=4 SYM, revealing a geometric structure involving intersecting lines and polygons in twistor space that simplifies amplitude calculations.

Contribution

It introduces a geometric interpretation of superamplitudes in twistor space, providing graphical rules for constructing amplitudes and analyzing their conformal properties.

Findings

N^kMHV amplitudes supported on intersecting lines in twistor space

Line moduli form lightlike polygons in moduli space

Triangulation rules lead to direct amplitude expressions

Abstract

We perform the twistor (half-Fourier) transform of all tree n-particle superamplitudes in N=4 SYM and show that it has a transparent geometric interpretation. We find that the N^kMHV amplitude is supported on a set of (2k+1) intersecting lines in twistor space and demonstrate that the corresponding line moduli form a lightlike (2k+1)-gon in moduli space. This polygon is triangulated into two kinds of lightlike triangles lying in different planes. We formulate simple graphical rules for constructing the triangulated polygons, from which the analytic expressions of the N^kMHV amplitudes follow directly, both in twistor and in momentum space. We also discuss the ordinary and dual conformal properties and the cancellation of spurious singularities in twistor space.