(In)validity of large N orientifold equivalence

TL;DR

This paper demonstrates that the large N orientifold equivalence between certain supersymmetric and QCD-like theories fails at small radius due to spontaneous symmetry breaking, highlighting the importance of symmetry realization conditions.

Contribution

It provides a concrete analysis showing the failure of large N orientifold equivalence at small radius through symmetry breaking considerations.

Findings

Large N equivalence fails at small radius due to charge conjugation symmetry breaking.

Unbroken charge conjugation symmetry is necessary for the equivalence to hold.

The validity of the equivalence depends on non-perturbative dynamics and symmetry realization.

Abstract

It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the $N\to\infty$ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N ``orientifold equivalence'' have appeared. By considering theories compactified on $R^3 \times S^1$, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on $R^4$ (or $ R^3 \times S^1$ for sufficiently large radius) is not currently known.