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

2009/07/23 by G.P. Korchemsky, G. P. Korchemsky, E. Sokatchev · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Geometry #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Particle physics theoretical and experimental studies #Physics #Polygon (computer graphics) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Space (punctuation) #Twistor space #Twistor theory #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2009.11.017

published as Nucl.Phys.B829:478-522,2010 · 46 pages, 17 figures

arxiv created 2009/07/23 · openalex publication_date 2009/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Exacting 𝒩 = 4 superconformal symmetry
• All next-to-maximally-helicity-violating one-loop gluon amplitudes inN=4super-Yang-Mills theory
• Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
• Loops in twistor space
• Generating tree amplitudes in 𝒩 = 4 SYM and 𝒩 = 8 SG
• Perturbative Gauge Theory As A String Theory In Twistor Space

Cited by

• The Yangian origin of the Grassmannian integral
• Delta functions on twistor space and their sign factors