Necessary and sufficient conditions for non-perturbative equivalences of large N_c orbifold gauge theories

Large N coherent state methods are used to study the relation between U(N_c) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N_c limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N_c dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N_c dynamics of the daughter theory, restricted to the untwisted sector invariant under ``theory space'' permutations, coincide. This implies equality, in the large N_c limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N_c equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N_c equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling [1].