Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra

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.

Calabi-Yau manifolds and SU(3) structure

“…Related discussions can also be found for example in Refs. [42,[55][56][57][58][59]. It would be interesting to explore if the methods used in these references can be useful to find the required source term.…”

N S-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes

“…13 The BI and resulting scalar equation are sometimes more complicated, depending on what exactly is F . For example, an additional constant next to the δ can be obtained, see for instance [85].…”

Smeared versus localised sources in flux compactifications

“…2 Here and in the following, δ(Op) is meant to implicity also include sums of parallel Op-planes. where δ n+1 (O(8 − n)) is shorthand for the normalized (n + 1) volume form transverse to the O(8 − n) orientifold plane multiplied by δ(O(8 − n)).…”

“…In the smeared limit these solutions either have an internal space that is Ricci-flat, being the D-dimensional generalisation of the GKP solution [1], or the solutions have a negatively curved twisted torus as internal space, being the D-dimensional generalisation of some solutions given in [19] (which themselves are T-dual to the GKP solution, see also [20]). The solutions on the twisted tori of [19] were obtained in the smeared limit and a discussion on their localisation was given in [2,3]. Here we discuss the D-dimensional generalisation of these solutions very explicitly from the point of view of the 10-dimensional equations of motion.…”