Yang-Mills Duality and the Generation Puzzle

TL;DR

This paper proposes a nonabelian duality in Yang-Mills theory as a solution to the fermion generation puzzle, suggesting a broken dual symmetry explains three generations and their properties, with testable predictions.

Contribution

It introduces a nonabelian generalization of electric-magnetic duality in Yang-Mills theory and links it to the fermion generation puzzle within the Standard Model.

Findings

Dual symmetry exists in classical Yang-Mills theory.

Broken dual symmetry may explain three fermion generations.

Calculations yield parameters consistent with experimental data.

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.