Twistors, strings and supersymmetric gauge theories

TL;DR

This thesis explores the computation of scattering amplitudes in N=4 super-Yang-Mills theory using twistor space, unitarity methods, and Wilson loop dualities, revealing new insights into their mathematical structure and loop-level relations.

Contribution

It provides a comprehensive review of twistor techniques, unitarity methods, and Wilson loop dualities applied to scattering amplitudes, including explicit two-loop calculations.

Findings

Two-loop six-point amplitude equals polygonal Wilson loop

Twistor space techniques simplify tree-level amplitude analysis

Wilson loop--scattering amplitude duality confirmed at two loops

Abstract

This thesis is concerned with the study of scattering amplitudes in four-dimensional conformal field theories, more particularly the N=4 super-Yang-Mills theory. We study this theory first at tree level by using twistor space techniques and review the twistor string models that were proposed to describe it. Then, we turn to the issue of iteration relations and all loop ansatze for scattering amplitudes. We review the unitarity method for computing scattering amplitudes and discuss the Wilson loop--scattering amplitude duality that was inspired by the strong-coupling prescription of Alday and Maldacena for scattering amplitudes. We describe in some detail the computation of a two-loop six-point scattering amplitude and its surprising equality to the polygonal Wilson loop.