Can large Nc equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?

TL;DR

This paper investigates the conditions under which large Nc equivalence holds between supersymmetric Yang-Mills theories and their orbifold projections, clarifying previous misconceptions and emphasizing the importance of symmetry realization.

Contribution

It establishes necessary and sufficient conditions for large Nc equivalence in orbifold projections, correcting prior assumptions about inequivalence for Z_2 projections.

Findings

Large Nc equivalence depends on unbroken discrete symmetries.

Z_k projections with k > 2 violate equivalence due to symmetry breaking.

Correct mapping of vacuum energies and theta angles resolves previous inconsistencies.

Abstract

Necessary and sufficient conditions for large Nc equivalence between parent and daughter theories, for a wide class of orbifold projections of U(Nc) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z_k projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multi-flavor generalizations. Z_k projections with k > 2 yielding chiral gauge theories violate the symmetry realization conditions needed for large Nc equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z_2 projections, we show that previous assertions of large Nc inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multi-valuedness in the mapping of theta parameters from parent to daughter.