Gauge Theories from Orientifolds and Large N Limit

TL;DR

This paper explores how string theory with D-branes and orientifolds in orbifolded space-time relates to large N gauge theories, showing that correlation functions simplify to those in ${ m N}=4$ theories and analyzing beta-function behaviors.

Contribution

It extends the understanding of gauge theories from string theory by including orientifolds, demonstrating the reduction of correlation functions to ${ m N}=4$ cases and analyzing large N limits for various supersymmetries.

Findings

Correlation functions in these theories reduce to those in ${ m N}=4$ theory.

Theories with vanishing beta-functions are identified in the large N limit.

Gauge coupling running is suppressed in non-vanishing beta-function theories at large N.

Abstract

Extending the recent work in hep-th/9803076, we consider string perturbative expansion in the presence of D-branes and orientifold planes imbedded in orbifolded space-time. In the $\alpha'\to 0$ limit the weak coupling string perturbative expansion maps to `t Hooft's large N expansion. We focus on four dimensional ${\cal N}=1,2,4$ supersymmetric theories, and also discuss possible extensions to ${\cal N}=0$ cases. Utilizing the string theory perturbation techniques we show that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ theory. In particular, we discuss theories (which are rather constrained) with vanishing beta-functions to all orders in perturbation theory in the large N limit. We also point out that in theories with non-vanishing beta-functions the gauge coupling running is suppressed in the large N limit. Introduction of orientifold planes allows to construct certain gauge theories with SO, Sp and SU gauge groups and various matter (only unitary gauge groups with bi-fundamental/adjoint matter arise in theories without orientifold planes).