An ambitwistor Yang-Mills Lagrangian

TL;DR

This paper develops a new ambitwistor space formulation of Yang-Mills theory using a Chern-Simons Lagrangian, resulting in a cubic-vertex action that aligns with standard theory and may underpin twistor-based recursion relations.

Contribution

It introduces an ambitwistor space Lagrangian for Yang-Mills theory that simplifies interactions to cubic vertices and connects to twistor diagram techniques.

Findings

Equivalent space-time action with cubic vertices

Explicit ambitwistor propagators and vertices derived

Potential foundation for twistor diagram recursion relations

Abstract

We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory.