Superstring Orientifolds with Torsion: O5 Orientifolds of Torus Fibrations and their Massless Spectra

TL;DR

This paper explores IIB orientifolds with O5 planes and D5 branes on T^2 fibrations, analyzing supersymmetry, fluxes, and massless spectra using an intrinsic approach and T-duality checks.

Contribution

It provides an intrinsic description of superstring orientifolds with torsion, extending previous T-duality analyses and detailing the massless spectra and geometric structures involved.

Findings

Examples with different supersymmetries (N=1,2,3) are constructed.

Internal geometries can have integrable or nonintegrable complex structures depending on fluxes.

Explicit massless spectra of gauge fields and moduli are identified.

Abstract

Using a ``Superstrings with Torsion'' type description, we study a class of IIB orientifolds in which spacefilling O5 planes and D5 branes wrap the T^2 fiber in a warped modification of the product of 4D Minkowski space and a T^2 fibration. For the case that the base is T^4, we provide examples that preserve 4D N = 1, 2, and 3 supersymmetry, both with internal RR flux, and with a combination of internal RR and NS flux. In these examples, the internal geometries admit integrable complex structure; however, the almost complex structure selected by the supersymmetry conditions is nonintegrable in the case that there is NS flux. We indicate explicitly the massless spectrum of gauge fields and moduli in each example. In a previous investigation, this class of orientifolds was studied using T-duality. Here, we extend the previous analysis, first by providing an intrinsic description that does not rely on duality, and then by elaborating on details of the T-duality map, which we use to check our results.