A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields

TL;DR

This paper introduces a generalized duality symmetry in 4D nonabelian Yang-Mills theory, revealing a dual potential framework that unifies electric and magnetic sources through a symmetric dual transform.

Contribution

It extends the concept of duality symmetry from electromagnetism to nonabelian gauge fields, providing a dual potential formalism and explicit dual transform in loop space variables.

Findings

Dual symmetry reduces to electromagnetism in special cases

Dual potentials describe monopoles and charges symmetrically

Standard equations of motion emerge from duality considerations

Abstract

It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport $\tilde{A}_\mu(x)$ constructed earlier for monopoles is seen to function also as a potential in giving full description of the gauge field, playing thus an entirely dual symmetric role to the usual potential $A_\mu(x)$. Sources of $A$ are monopoles of $\tilde{A}$ and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equations for respectively the classical and Dirac point charge; this applies whether the charge is electric or magnetic, the two cases being related just by a dual transform. The dual transformation itself is explicit, though somewhat complicated, being given in terms of loop space variables of the Polyakov type.