From Twistor Actions to MHV Diagrams

TL;DR

This paper demonstrates that MHV diagrams can be derived from twistor actions in an axial gauge, extending the formalism to include matter fields and revealing a larger gauge symmetry.

Contribution

It introduces a twistor action framework for gauge theories that naturally produces MHV diagrams and extends this to matter fields, revealing new MHV vertices.

Findings

MHV diagrams are Feynman diagrams of twistor actions in an axial gauge

Extended twistor actions include matter fields with new MHV vertices

Larger gauge symmetry in twistor space enables a manifest MHV formalism

Abstract

We show that MHV diagrams are the Feynman diagrams of certain twistor actions for gauge theories in an axial gauge. The gauge symmetry of the twistor action is larger than that on space-time and this allows us to fix a gauge that makes the MHV formalism manifest but which is inaccessible from space-time. The framework is extended to describe matter fields: as an illustration we explicitly construct twistor actions for an adjoint scalar with arbitrary polynomial potential and a fermion in the fundamental representation and show how this leads to additional towers of MHV vertices in the MHV diagram formalism.