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

TL;DR

This work analyzes large $N_c$ orbifold equivalence between a parent ${\cal N}=1$ supersymmetric Yang–Mills theory and its ${\mathbb Z}_2$ orbifold daughter, clarifying the precise mappings of couplings, masses, theta angles, and observables. It shows that when these mappings are correctly implemented, including a multi-valued theta connection, the vacuum energy, topological susceptibility, and anomaly structures align between the theories, supporting nonperturbative equivalence in infinite volume. The paper further demonstrates how domain walls and vacuum structure map between parent and daughter, and explains failures for ${\mathbb Z}_k$ with $k>2$ and for ${\cal N}=4$ cases due to spontaneous symmetry breaking. Overall, the authors argue that large-$N$ equivalence remains viable for the ${\mathbb Z}_2$ projection of ${\cal N}=1$ SYM and its multiflavor generalizations, while providing precise criteria and mappings for when it may or may not hold. They also discuss implications for lattice tests and address conflicting claims in prior literature by emphasizing correct observable mappings.

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.