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A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields

Chan Hong-Mo·J. Faridani·Tsou Sheung Tsun
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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 $\tilde{A}_μ(x)$ 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 $A_μ(x)$. 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.

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Chan Hong-Mo, J. Faridani, Tsou Sheung Tsun. 1995-12-22. A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields. https://doi.org/10.1103/physrevd.53.7293

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