Form factors and correlation functions in N = 4 super Yang-Mills theory from twistor space

TL;DR

This thesis extends twistor formalism to off-shell quantities in N=4 super Yang-Mills, enabling computation of form factors and exploring integrability via the one-loop dilatation operator.

Contribution

It introduces a twistor-based approach for off-shell operators, allowing calculation of form factors beyond tree level and analyzing integrability properties.

Findings

All gauge-invariant operators generate tree-level MHV form factors.

Computed NMHV and higher form factors using twistor formalism.

Derived the one-loop dilatation operator in twistor space.

Abstract

In this PhD thesis we extend the twistor formalism to encompass (partially) off-shell quantities. We describe all gauge-invariant local composite operators in twistor space and show that they immediately generate all tree-level form factors of the MHV type. We use the formalism to compute form factors at NMHV and higher NkMHV level in parallel to how this had been done for amplitudes previously. Finally, we move on to integrability by computing the one-loop dilatation operator in the scalar sector of the theory in twistor space.