The self-dual sector of QCD amplitudes

TL;DR

This paper presents a simplified action for self-dual Yang-Mills theory that captures a subset of amplitudes, making higher-loop amplitude vanishing explicit and providing a clearer perturbative S-matrix, with analogous results for gravity.

Contribution

It introduces a minimalistic action for self-dual Yang-Mills theory that simplifies the analysis of amplitudes and clarifies the structure of the perturbative S-matrix.

Findings

One-loop amplitudes in self-dual theory are a subset of Yang-Mills amplitudes.

Higher-loop amplitudes vanish explicitly in this formulation.

The approach applies similarly to gravity, simplifying their amplitude analysis.

Abstract

We provide an action for self-dual Yang-Mills theory which is a simple truncation of the usual Yang-Mills action. Only vertices that violate helicity conservation maximally are included. One-loop amplitudes in the self-dual theory then follow as a subset of the Yang-Mills ones. In light-cone gauges this action is almost identical to previously proposed actions, but in this formulation the vanishing of all higher-loop amplitudes is obvious; the explicit perturbative S-matrix is known. Similar results apply to gravity.