An ambitwistor Yang-Mills Lagrangian
L. J. Mason, D. Skinner
TL;DR
This work formulates Yang–Mills theory as a holomorphic Chern–Simons theory on ambitwistor space restricted to an 8‑dimensional CR submanifold associated with Euclidean space. By deriving a space–time action with auxiliary fields, it shows equivalence to standard YM and yields a perturbative expansion with only trivalent vertices, naturally aligning with BCFW recursion and twistor‑diagram approaches. The paper provides explicit space‑time and momentum‑space Feynman rules, a clear propagator structure, and a bridge to potential ambitwistor‑string formulations, highlighting the generating principle for gauge‑theory amplitudes from twistor geometry.
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.