  Recently, an attractive model of GUT breaking has been proposed in which a 5
dimensional supersymmetric SU(5) gauge theory on an S^1/(Z_2\times Z_2')
orbifold is broken down to the 4d MSSM by SU(5)-violating boundary conditions.
Motivated by this construction and several related realistic models, we
investigate the general structure of orbifolds in the effective field theory
context, and of this orbifold symmetry breaking mechanism in particular. An
analysis of the group theoretic structure of orbifold breaking is performed.
This depends upon the existence of appropriate inner and outer automorphisms of
the Lie algebra, and we show that a reduction of the rank of the GUT group is
possible. Some aspects of larger GUT theories based on SO(10) and E_6 are
discussed. We explore the possibilities of defining the theory directly on a
space with boundaries and breaking the gauge symmetry by more general
consistently chosen boundary conditions for the fields. Furthermore, we derive
the relation of orbifold breaking with the familiar mechanism of Wilson line
breaking, finding a one-to-one correspondence, both conceptually and
technically. Finally, we analyse the consistency of orbifold models in the
effective field theory context, emphasizing the necessity for self-adjoint
extensions of the Hamiltonian and other conserved operators, and especially the
highly restrictive anomaly cancellation conditions that apply if the bulk
theory lives in more than 5 dimensions.
