  When the extra dimensional space is not simply-connected, dynamics of the AB
phase in the extra dimension can induce dynamical gauge symmetry breaking by
the Hosotani mechanism. This opens up a new way of achieving unification of
gauge forces. It leads to the gauge-Higgs unification. The Hosotani mechanism
can be established nonperturbatively by lattice simulations, in which
measurements of the Polyakov line give a clue.
