  Grand unified theory defined on higher-dimensional orbifolds provides a new
way to solve the hierarchy problem. In gauge theory on an orbifold many
different sets of boundary conditions imposed at orbifold fixed points (branes)
are related by large gauge transformations, forming an equivalent class of
boundary conditions. Thanks to the Hosotani mechanism the physics remains the
same in all theories in a given equivalent class, though the symmetry of
boundary conditions differs from each other. Quantum dynamics of Wilson line
phases rearranges the gauge symmetry. In the nonsupersymmetric SU(5) model the
presence of bulk fermions leads to the spontaneous breaking of color SU(3). In
the supersymmetric model with Scherk-Schwarz SUSY breaking, color SU(3) is
spontaneously broken even in the absence of bulk fermions if there are Higgs
multiplets.
