A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields

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.

Latex file, 26 pages, 3 figures and 2 charts not included but supplied on request

References in corpus (25)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• A Strong Coupling Test of S-Duality
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics
• Duality Symmetric Actions
• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• Exact Superpotentials, Quantum Vacua and Duality in Supersymmetric SP(N_c) Gauge Theories
• On Duality in Supersymmetric Yang-Mills Theory
• On Non-Abelian Duality
• Phases of N=1 supersymmetric gauge theories in four dimensions
• Electric Magnetic Duality in String Theory
• New Examples of Duality in Chiral and Non-Chiral Supersymmetric Gauge Theories
• Quantization of Dyon Charge and Electric-Magnetic Duality in String Theory
• Reducing $S$- duality to $T$- duality
• New RG Fixed Points and Duality in Supersymmetric SP(N_c) and SO(N_c) Gauge Theories
• Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String Theory
• S-Duality in Gauge Theories as a Canonical Transformation
• T-duality and spacetime supersymmetry
• S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,
• A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality
• Remarks on Non-Abelian Duality in N=1 Supersymmetric Gauge Theories
• Duality and the Legendre Transform
• From Quantum Monodromy to Duality

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