Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality

TL;DR

This paper investigates six and four-dimensional ${ m N}=1$ supersymmetric orientifolds of Type IIB on orbifolds, highlighting the importance of non-perturbative sectors and dualities in understanding their consistency and tadpole cancellation.

Contribution

It identifies conditions where the perturbative approach is sufficient and emphasizes the role of non-perturbative sectors in orientifolds, using F-theory and heterotic duality to analyze their properties.

Findings

Non-perturbative sectors are crucial in many orientifolds.

Naive tadpole conditions may lack solutions due to non-perturbative effects.

Duality tools help identify consistent chiral ${ m N}=1$ vacua.

Abstract

We consider six and four dimensional ${\cal N}=1$ supersymmetric orientifolds of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, and list the four dimensional ${\cal N}=1$ orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain non-perturbative sectors that are missing in the world-sheet approach. These non-perturbative sectors can be thought of as arising from D-branes wrapping various collapsed 2-cycles in the orbifold. Using these observations, we explain certain ``puzzles'' in the literature on four dimensional orientifolds. In particular, in some four dimensional orientifolds the ``naive'' tadpole cancellation conditions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadequate in these cases due to appearance of additional non-perturbative sectors. The main tools in our analyses are the map between F-theory and orientifold vacua and Type I-heterotic duality. Utilizing the consistency conditions we have found in this paper, we discuss consistent four dimensional chiral ${\cal N}=1$ Type I vacua which are non-perturbative from the heterotic viewpoint.