Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns

TL;DR

This paper introduces a novel coupling of nonlinear sigma models with Yang-Mills fields, leading to new symmetry breaking patterns and Higgs-less mass generation mechanisms in gauge theories.

Contribution

It extends gauge field theory by incorporating nonlinear sigma model fields as dynamical entities, enabling new symmetry breaking patterns without Higgs particles.

Findings

Couples nonlinear sigma models to Yang-Mills fields on cosets of U(N).

Identifies distinct chiral symmetry breaking patterns.

Proposes Higgs-less mass generation mechanisms.

Abstract

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation, but for the non-Abelian case. Here we study the case of internal gauge symmetry groups, in particular, unitary groups U(N). We show how to couple standard Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex projective, Grassman and flag manifolds. These different couplings lead to distinct (chiral) symmetry breaking patterns and \emph{Higgs-less} mass-generating mechanisms for Yang-Mills fields.