A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality

Abstract

The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is a dual potential, but it is a 2-indexed tensor $T_{\mu \nu }$ of the Freedman-Townsend type. Though not itself functioning as such, $T_{\mu \nu }$ gives rise to a dual parallel transport, ${\tilde{A}}_{\mu }$, for the phase of the wave function of the colour magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard colour (electric) charge itself is found to be a monopole of ${\tilde{A}}_{\mu }$. At the same time, the gauge symmetry is found doubled from say $SU(N)$ to $SU(N)\times SU(N)$. A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a `universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov (1980).

We regret that, due to a technical hitch, parts of the reference list were mixed up. This is the corrected version. We apologize to the authors whose papers were misquoted

References in corpus (10)

• 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
• Duality Symmetric Actions
• On Non-Abelian Duality
• Phases of N=1 supersymmetric gauge theories in four dimensions
• Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String Theory
• S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,
• Remarks on Non-Abelian Duality in N=1 Supersymmetric Gauge Theories

Cited by in corpus (23)

• S-Duality in Gauge Theories as a Canonical Transformation
• A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields
• Physical Consequences of Nonabelian Duality in the Standard Model
• Deformations of duality-symmetric theories
• Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
• Particle Motion in a Yang-Mills Field: Wong's Equations and Spin One-half Analogues
• Local symmetries of the non-Abelian two-form
• Classical Duality in Gauge Theories
• Dual symmetry in a generalized Maxwell theory
• Topological Defects in a Deformed Gauge Theory
• A dual view of the 3d Heisenberg model and the abelian projection
• Nonabelian Generalization of Electric-Magnetic Duality - a Brief Review
• Gauge transformations of the non-Abelian two-form
• Are Preons Dyons? Naturalness of Three Generations
• Proton spin: a topological invariant
• Pursuing Gravitational S-Duality
• Monopoles in Superloop Space
• Supersymmetric Duality in Deformed Superloop Space
• Polyakov Loops for the ABJ Theory
• Generalized dual symmetry of nonabelian theories and the freezing of α_s
• Phase transition in the Higgs model of scalar dyons
• Superunitary operator and BRST transformations for non-Abelian two-form
• Dualized Gravity beyond Linear Approximation