Lattice gauge-higgs theories with local x global symmetry groups including exact solutions

We discuss a class of lattice gauge-Higgs models with local x global symmetry groups. These may also be viewed as a new class of disordered spin models. We give general properties of these theories and present exact solutions for certain (infinite) classes of discrete 2D models. Given the strong gauge coupling limit involved, the latter constitute the first nontrivial exactly solved gauge-Higgs theories. Our results provide the first existence proof of theories which satisfy a necessary condition of realistic gauge-Higgs models, namely that the mass gaps for the Higgs and gauge sectors must both vanish and their ratio must approach a finite constant, in the continuum limit.