A cubic action for self-dual Yang-Mills

TL;DR

This paper introduces a new cubic action formulation for self-dual Yang-Mills theory, simplifying the derivation of field equations and revealing a unique scattering amplitude structure consistent with string theory predictions.

Contribution

It presents a novel cubic action for self-dual Yang-Mills, differing from previous models, and demonstrates its consistency with known scattering amplitudes.

Findings

The cubic action yields the same non-vanishing three-particle amplitude as string theory.

The interaction vertex differs from previous formulations based on N=2 string.

Perturbation theory confirms the unique scattering amplitude structure.

Abstract

We make a change of field variables in the J formulation of self-dual Yang--Mills theory. The field equations for the resulting algebra valued field are derivable from a simple cubic action. The cubic interaction vertex is different from that considered previously from the N=2 string, however, perturbation theory with this action shows that the only non-vanishing connected scattering amplitude is for three external particles just as for the string.