Strings on orientifolds

We construct several examples of compactification of type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with N = 1 supersymmetry, multiple tensor multiplets, and different gauge groups. In nine dimensions we obtain a model that is dual to M-theory compactified on a Klein bottle.     

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2$N=2$ minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Notes on discrete torsion in orientifolds

In this paper we discuss discrete torsion in orientifolds. In particular, we apply the physical understanding of discrete torsion worked out several years ago, as group actions on B$B$ fields, to the case of orientifolds, and recover some old results of Braun and Stefanski concerning group cohomology and twisted equivariant K theory. We also derive new results including phase factors for nonorientable worldsheets and analogues for C$C$ fields.     

Gravitational couplings and Z2 orientifolds

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low-dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold d-planes can be understood in terms of flux quantization of the d − 3 form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on T⁶/Z₂, which is dual to F-theory on a complex 4-fold with terminal singularities.     

Remarks on global anomalies in RCFT orientifolds

We check the list of supersymmetric standard model orientifold spectra of Dijkstra, Huiszoon and Schellekens for the presence of global anomalies, using probe branes. Absence of global anomalies is found to impose strong constraints, but in nearly all cases they are automatically satisfied by the solutions to the tadpole cancellation conditions.     

Hierarchies from D-brane instantons in globally defined Calabi-Yau orientifolds

We construct the first globally consistent semirealistic type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of nonperturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.     

Type IIB orientifolds,D‐brane instantons and the LARGE volume scenario

This review article is concerned with three topics important for the construction of four‐dimensional models of particle physics in the context of type II String Theories. Special emphasis is put on a consistent presentation of these topics as well as on highlighting their interconnections. The first of the three topics deals with the tadpole cancellation conditions and the cancellation of chiral anomalies for type IIB orientifolds with orientifold three‐ and seven‐planes. The second topic is related to non‐perturbative effects originating from D‐brane instantons. In particular, in the presence of a realistic particle physics sector, a chiral zero‐mode constraint for contribution of instantons to the superpotential arises. The third topic is about moduli stabilisation in type IIB string compactifications. Two scenarios, the KKLT and Large Volume Scenario, are reviewed and a model for the latter scenario with the chiral zero‐mode constraint taken into account is presented.     

Searching for K3 fibrations

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyze 184 026 such spaces and identify among them the 124 701 which are K3 fibrations. As some of the weights give rise to two or three distinct types of fibrations, the total number we find is 167 406. With our methods one can also study elliptic fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of the 3-folds obtaining more than three times as many as were previously known.     

Instantons and mirror K3 surfaces

The instanton moduli space of a real 4-dimensional torus is an 8-dimensional Calabi-Yau manifold. Associated to this Calabi-Yau manifold are two (singular) K3 surfaces, one a quotient, the other a submanifold of the moduli space; both carry a natural Calabi-Yau metric. They are curiously related in much the same way as special examples of complex 3-dimensional mirror manifolds; however, in our case the mirror is present in the form of instanton moduli.