Dynamical Gauge Boson and Strong-Weak Reciprocity

TL;DR

This paper proposes a framework where asymptotically nonfree gauge theories are interpreted as theories of composite gauge bosons, demonstrating masslessness, universality, and coexistence with free gauge bosons through explicit models and calculations.

Contribution

It introduces a novel interpretation of nonfree gauge theories as composite gauge boson theories with hidden local symmetry, supported by explicit model calculations and a reciprocal relation between couplings.

Findings

Massless gauge bosons with universal coupling are realized.

Existence of a critical coupling restoring hidden local symmetry.

Coexistence of asymptotic free and nonfree gauge bosons with related couplings.

Abstract

It is proposed that asymptotically nonfree gauge theories are consistently interpreted as theories of composite gauge bosons. It is argued that when hidden local symmetry is introduced, masslessness and coupling universality of dynamically generated gauge boson are ensured. To illustrate these ideas we take a four dimensional Grassmannian sigma model as an example and show that the model should be regarded as a cut-off theory and there is a critical coupling at which the hidden local symmetry is restored. Propagator and vertex functions of the gauge field are calculated explicitly and existence of the massless pole is shown. The beta function determined from the $ Z $ factor of the dynamically generated gauge boson coincides with that of an asymptotic nonfree elementary gauge theory. Using these theoretical machinery we construct a model in which asymptotic free and nonfree gauge bosons coexist and their running couplings are related by the reciprocally proportional relation.