Gauge Symmetry Breaking: Hosotani Mechanism On Lattice
Abstract: Unification of forces is unification of gauge interactions. Large gauge symmetry is spontaneously broken to smaller gauge symmetry, which is conventionally achieved by the Higgs mechanism of scalar fields. Alternatively dynamical gauge symmetry breaking can be achieved by dynamics of Aharonov-Bohm phases of gauge fields in extra dimensions. It is called the Hosotani mechanism. We show how it works not only in perturbation theory in the continuum, but also nonperturbatively in the lattice gauge theory by numerical simulations. The Hosotani mechanism is characterized as gauge symmetry breaking by gauge invariant quantities.