Yang-Mills Duality and the Generation Puzzle

Abstract

The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of electric-magnetic duality. First, by constructing in loop space a nonabelian generalization of the abelian dual transform (Hodge *), one finds that a ``magnetic'' symmetry exists also in classical Yang-Mills theory dual to the original (``electric'') gauge symmetry. Secondly, from a result of 't Hooft's, one obtains that for confined colour SU(3), the dual symmetry $\widetilde{SU}(3)$ is spontaneously broken and can play the role of the ``horizontal symmetry'' for generations. Thirdly, such an identification not only offers an explanation why there should be three and apparently only three generations of fermions with the remarkable mass and mixing patterns seen in experiment, but allows even a calculation of the relevant parameters giving very sensible results. Other testible predictions follow ranging from rare hadron decays to cosmic ray air showers.

19 pages, Latex, 4 figures, invited lecture at the Intern. Conf. on Fundamental Sciences: Mathematics and Theoretical Physics, March 2000, Singapore; Fig 4 changed

References in corpus (4)

• Initial Results from the CHOOZ Long Baseline Reactor Neutrino Oscillation Experiment
• Extension of the Cosmic-Ray Energy Spectrum Beyond the Predicted Greisen-Zatsepin-Kuz'min Cutoff
• Possible Test for the Suggestion that Air Showers with $E>10^{20}$ eV are due to Strongly Interacting Neutrinos
• A Dynamical Mechanism for Quark Mixing and Neutrino Oscillations