Gauge Theories from Orientifolds and Large N Limit

TL;DR

The paper develops a framework in which large $N$ gauge theories with ${ m SU}(N)$, ${ m SO}(N)$, and ${ m Sp}(N)$ gauge groups arising from Type IIB string theory on orbifolds and orientifolds can be studied via perturbative string techniques. It extends the BKV correspondence between string world-sheets and 't Hooft planar diagrams to include orientifolds, showing that many correlators in ${ m N}<4$ theories reduce to calculations in the parent ${ m N}=4$ theory in the large $N$ limit, provided tadpole cancellation holds. The authors construct explicit ${ m N}=2$ superconformal theories from even and odd orbifold orders and demonstrate ${ m N}=1$ models with vanishing beta functions at large $N$ using ${f Z}_2 imes{f Z}_2$ orientifolds, while also discussing nonfinite cases and theories without a worldsheet description. Overall, the work highlights how string perturbation theory and orientifold technology yield powerful finiteness and reduction results in large $N$ gauge theories, with concrete realizations for SO/Sp groups and diverse matter content. This has potential implications for understanding conformal windows, dualities, and the large $N$ dynamics of gauge theories via string-theoretic constructions.

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 $α'\to 0$ 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).

Figures (3)

• Figure 1: A planar diagram.
• Figure 2: Tree-channel Klein bottle, Möbius strip and annulus amplitudes.
• Figure 3: Factorization of the Klein bottle, Möbius strip and annulus amplitudes.