Universal Yang-Mills Action on Four Dimensional Manifolds

TL;DR

This paper introduces a universal non-linear Yang-Mills action on four-dimensional manifolds that naturally separates into self-dual and anti-self-dual components, simplifying the derivation of related equations.

Contribution

It proposes a new non-linear generalization of the Yang-Mills action that automatically splits into self-dual and anti-self-dual parts, facilitating analysis without solving equations of motion.

Findings

Action naturally separates into self-dual and anti-self-dual parts

Derives self-dual and anti-self-dual equations without solving equations of motion

Potential applicability to non-commutative Yang-Mills theories

Abstract

The usual action of Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four dimensional manifolds. The non-linear generalization which is known as the Born-Infeld action has been given. In this paper we give another non-linear generalization on four dimensional manifolds and call it a universal Yang-Mills action. The advantage of our model is that the action splits {\bf automatically} into two parts consisting of self-dual and anti-self-dual directions. Namely, we have automatically the self-dual and anti-self-dual equations without solving the equations of motion as in a usual case. Our method may be applicable to recent non-commutative Yang-Mills theories studied widely.