Scattering Amplitudes and Wilson Loops in Twistor Space

TL;DR

This review discusses recent advances in twistor space methods for calculating scattering amplitudes and Wilson loops in N=4 super Yang-Mills theory, highlighting new derivations and connections to geometric structures.

Contribution

It presents a derivation of MHV rules from the twistor action and constructs momentum twistor space loop integrands as Wilson loop expectation values, linking various twistor-based approaches.

Findings

Derivation of MHV rules from twistor action.

Construction of momentum twistor space loop integrands.

Connection between Wilson loops and correlation functions.

Abstract

This article reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for N=4 super Yang-Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang-Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrcek and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This article is an invited review for a special issue of Journal of Physics A devoted to `Scattering Amplitudes in Gauge Theories'.