Nonlinear models as gauge theories

In the usual formulation of nonlinear models (such as chiral models), there is invariance under a nonlinear realization of a group $G_F$ which becomes linear when restricted to a subgroup $H_F$. We formulate them so that they become gauge theories for a local group ${\mathcal{H}}_C$. It is the local version of a global group $H_C$. When the gauge transformations are unrestricted at spatial infinity, only $H_C$ singlets are observable, and the usual formulation is recovered. When the gauge transformations are required to reduce to identity at spatial infinity, the usual formulation is no longer recovered. In particular, (1) nonsinglets under $H_C$ become observable, (2) the classical vacuum becomes degenerate under suitable conditions as in Yang-Mills theories, (3) the spontaneous symmetry breakdown of $G_F$ seems complete. (In the usual formulations, $G_F$ is broken down only to $H_F$.) It is shown that the instanton and meron solutions of Yang-Mills theories are also solutions of certain nonlinear models. It is also shown that in a certain class of nonlinear models in (Euclidean) (3 + 1)-dimensional space-time, there are no instanton solutions for any choice of the groups.