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

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

2008-09-11

arxiv.org/abs/0809.2077v1

J. Nonlinear Math. Phys.15:91-101, 2008

Physics

High Energy Physics

High Energy Physics - Theory

11 pages. To appear in Journal of Nonlinear Mathematical Physics

Scientific paper

10.2991/jnmp.2008.15.s3.10

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.

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