On Large N Gauge Theories from Orientifolds

TL;DR

The authors classify four-dimensional ${\cal N}=1$ gauge theories arising from orientifolds of Type IIB on ${\bf C}^3/\Gamma$ with Abelian $\Gamma$, identifying a small set of orbifolds that admit a perturbative world-sheet description. In the large-$N$ limit, the correlation functions of these theories reduce to those of the parent ${\cal N}=4$ oriented theory, with many subtleties arising from tadpole cancellation and wrapped-brane states. They show that only six Abelian groups ($\mathbf{Z}_3$, $\mathbf{Z}_7$, $\mathbf{Z}_3\otimes\mathbf{Z}_3$, $\mathbf{Z}_2\otimes\mathbf{Z}_2$, $\mathbf{Z}_2\otimes\mathbf{Z}_2\otimes\mathbf{Z}_3$, and $\mathbf{Z}_2\otimes\mathbf{Z}_3$) yield perturbative orientifolds after blow-ups, with the rest featuring non-perturbative sectors that prevent a purely world-sheet description. Local non-compact analyses and Type I–heterotic duals corroborate these results and align with field-theory expectations, providing a string-theoretic check of perturbative versus non-perturbative structures in large-$N$ gauge theories.

Abstract

We consider four dimensional ${\cal N}=1$ supersymmetric gauge theories obtained via orientifolds of Type IIB on Abelian C^3/G orbifolds. We construct all such theories that have well defined world-sheet expansion. The number of such orientifolds is rather limited. We explain this fact in the context of recent developments in four dimensional Type IIB orientifolds. In particular, we elaborate these issues in some examples of theories where world-sheet description is inadequate due to non-perturbative (from the orientifold viewpoint) states arising from D-branes wrapping (collapsed) 2-cycles in the orbifold. We find complete agreement with the corresponding statements recently discussed in the context of Type I compactifications on toroidal orbifolds. This provides a non-trivial check for correctness of the corresponding conclusions. We also find non-trivial agreement with various field theory expectations, and point out their origin in string language. The orientifold gauge theories that do possess well defined world-sheet description have the property that in the large N limit computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ oriented theory.