Nonlinear realization and hidden local symmetries

Bando, Kugo.

The idea of dynamical gauge bosons of hidden local symmetries in nonlinear sigma models is reviewed. Starting with a fresh look at the Goldstone theorem and low energy theorems, we present a modern review of the general theory of nonlinear realization both in nonsupersymmetric and supersymmetric cases. We then show that any nonlinear sigma model based on the manifold GIH is gauge equivalent to a “linear” model possessing a Gglobal x JJtocll symmetry, ffloc>l being a hidden local symmetry. The corresponding supersymmetric formulation is also presented. The above gauge equivalence can be extended to a model having a larger symmetry Gglobal x Gloc,,. Also reviewed are dynamical calculations showing that in some two-, three- and four-dimensional models, the gauge bosons of the hidden local symmetries acquire the kinetic terms via quantum effects, thus becoming “dynamical”. We suggest that such a dynamical gauge boson may be a rather common phenomenon realized in Nature. As a realistic example, we examine the QCD case where we identify the vector mesons (p, u, , K*) with the dynamical gauge bosons of the hidden UC)v local symmetry in the UC)L x UC)R/UC)V nonlinear sigma model. The totality of the vector meson phenomenology seems to support our basic idea. The axial-vector mesons are also incorporated into our framework. Also given is a brief sketch of some applications of this formalism to unified models beyond the standard model, such as technicolor, composite W/Z boson and supergravity models.