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

TL;DR

This paper establishes the precise conditions under which large N orbifold gauge theories are non-perturbatively equivalent, focusing on symmetry realization and extending previous proofs beyond strong coupling regimes.

Contribution

It proves that unbroken orbifold and permutation symmetries are sufficient for large N equivalence, extending earlier results to more general phases.

Findings

Large N dynamics coincide under symmetry conditions

Connected correlation functions are equal in parent and daughter theories

Symmetry breaking invalidates large N equivalence

Abstract

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N 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 equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.