We describe a simple and robust mechanism that stabilizes all Kahler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G_2 compactifications of M-theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kahler moduli are worked out. We find that the stabilized volumes of all two- and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.
We evaluate string one-loop contributions to the Einstein-Hilbert term in toroidal minimally supersymmetric type IIB orientifolds with D-branes. These have potential applications to the determination of quantum corrections to the moduli Kahler metric in these models.
We discuss the first step in the moduli stabilization program a la KKLT for a general class of resolved toroidal type IIB orientifolds. In particular, we discuss their geometry, the topology of the divisors relevant for the D3-brane instantons which can contribute to the superpotential, and some non--trivial aspects of the orientifold action.
We consider compact four-dimensional ${\bf Z_N}\times {\bf Z_M}$ type IIB orientifolds, for certain values of $N$ and $M$. We allow the additional feature of discrete torsion and discuss the modification of the consistency conditions arising from tadpole cancellation. We point out the differences between the cases with and without discrete torsion.
The zero mode structure for the generation of poly-instanton corrections for Euclidian D3-branes wrapping complex surfaces in Type IIB orientifolds with O7- and O3-planes is analyzed. Working examples of such surfaces and explicit embeddings into compact Calabi-Yau threefolds are presented, with special emphasis on geometries capable of realizing the LARGE volume scenario.
We construct boundary state and crosscap state in D=4,N=1 type-IIB Z_N orientifold and investigate properties of amplitude. We find that the boundary state of a cylinder is different from the boundary state of a Möbius strip. Using these states, we find that amplitudes do not factorize in Z_N(N=even) orientifold. Tadpole divergence remain in Z_4, Z_8, Z'_8 and Z'_{12} model due to volume dependence of boundary and crosscap state. On the other hand the amplitude of Z_3 and Z_7 orientifolds factorize so that we obtain the gauge groups of the model by employing the massless tadpole cancellation c…
We study the weak gravity conjecture, the swampland distance conjecture and the emergence proposal for $\mathcal{N}=1$ orientifold compactifications of type IIB string theory with O3-/O7-planes. We allow for orientifold projections with $h^{2,1}_+\neq 0$ which gives rise to closed-string $U(1)$ gauge fields, and our findings show that certain structures present for $\mathcal N=2$ compactifications are not present for $\mathcal N=1$. In particular, assumptions about stability have to be relaxed and we encounter an ambiguity for the emergence of gauge symmetries associated with the $h^{2,1}_+$ s…
We analyze the large N supergravity descriptions of the class of type IIB models T-dual to elliptic type IIA brane configurations containing two orientifold 6-planes and up to two NS 5-branes. The T-dual IIB configurations contain N D3-branes in the background of an orientifold 7-plane and, in some models, a Z_2 orbifold and/or D7-branes, which give rise to four-dimensional N=2 (or N=4) gauge theories with at most two factors. We identify the chiral primary states of the supergravity theories, and match them to gauge invariant operators of the corresponding superconformal theories using Maldac…
We discuss flux quantization and moduli stabilization in toroidal type IIB Z_N - or Z_N x Z_M -orientifolds, focusing mainly on their orbifold limits. After presenting a detailed discussion of their moduli spaces and effective actions, we study the supersymmetric vacuum structure of these models and derive criteria for the existence of stable minima. Furthermore, we briefly investigate the models away from their orbifold points and comment on the microscopic origin of their non-perturbative superpotentials.
We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational $α'^3$-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of $O3/O7$-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inf…
We analyze the properties of a spontaneously broken D=4, N=4 supergravity without cosmological constant, obtained by gauging translational isometries of its classical scalar manifold. This theory offers a suitable low energy description of the super-Higgs phases of certain Type-IIB orientifold compactifications with 3-form fluxes turned on. We study its N=3,2,1,0 phases and their classical moduli spaces and we show that this theory is an example of no-scale extended supergravity.
Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such vacua. By taking additional gaugino condensation on fixed space-time filling D3-branes into account also models without complex structure can be consistently stabilized to Minkowski vacua.
We consider the compactification of type IIB superstring theory on K3 $\times$ K3. We obtain the massless spectrum of the resulting two dimensional theory and show that the model is free of gravitational anomaly. We then consider an orbifold and an orientifold projection of the above model and find that their spectrum match identically and are anomaly-free as well. This gives a dual pair of type IIB theory in two dimensions and can be understood as a consequence of SL(2, Z) symmetry of the ten dimensional theory. We also point out the M-theory duals of the type IIB compactifications considered…
We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric type IIB orientifold vacua with D3- and D7-branes. After a general discussion of possible choices of fluxes allowing for stabilizing of a part of the moduli, we determine the resulting effective action including all soft supersymmetry breaking terms. We also extend the computation of our previous work concerning the matter field metrics arising from various open string sectors, in particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the F-theory lift of our constructions is investigated.
We study the IIB engineering of N=1 gauge theories with unitary gauge group and matter in the adjoint and (anti)symmetric representations. We show that such theories can be obtained as Z2 orientifolds of Calabi-Yau A2 fibrations, and discuss the explicit T-duality transformation to an orientifolded Hanany-Witten construction. The low energy dynamics is described by a geometric transition of the orientifolded background. Unlike previously studied cases, we show that the orientifold 5-`plane' survives the transition, thus bringing a nontrivial contribution to the effective superpotential. We ext…
We reconsider the two-point string scattering amplitudes of massless Neveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theory on the disk and projective plane in ten dimensions and analyse its $α'$ expansion. We also discuss the unoriented Type IIB theory on $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scattering amplitudes of the complex Kähler moduli and complex structures of the untwisted sector are computed on the disk and projective plane. New results are obtained together with known ones. Finally, we compare string scattering amplitudes results at $α'…
We derive the 3D N=1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric AdS$_3$ vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the shape moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in …
We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we pr…
We consider six dimensional N=1 space-time supersymmetric Type IIB orientifolds with non-zero untwisted NS-NS sector B-field. The B-field is quantized due to the requirement that the Type IIB spectrum be left-right symmetric. The presence of the B-field results in rank reduction of both 99 and 55 open string sector gauge groups. We point out that in some of the models with non-zero B-field there are extra tensor multiplets in the Z_2 twisted closed string sector, and we explain their origin in a simple example. Also, the 59 open string sector states come with a multiplicity that depends on the…
We study novel type IIB compactifications on the T^6/Z_2 orientifold. This geometry arises in the T-dual description of Type I theory on T^6, and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel the RR tadpoles either partially or fully by turning on three-form flux in the compact geometry. The resulting (super)potential for moduli is calculable. We demonstrate that one can find many examples of N=1 supersymmetric vacua with greatly reduced numbers of moduli in this system. A few examples with N>1 supersymmetry or complete supersymmetry breaking are…
We provide a detailed correspondence between G_4 gauge fluxes in F-theory compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models we classify the factorisable G_4-fluxes and match them with the set of universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U(1). In U(1)-restricted Tate models extra massless abelian fluxes exist which are associated with speci…
We consider Type IIB orientifold models on Calabi-Yau spaces with three-form G-flux turned on. These fluxes freeze some of the complex structure moduli and the complex dilaton via an F-term scalar potential. By introducing pairs of D9-anti-D9 branes with abelian magnetic fluxes it is possible to freeze also some of the Kaehler moduli via a D-term potential. Moreover, such magnetic fluxes in general lead to chiral fermions, which make them interesting for string model-building. These issues are demonstrated in a simple toy model based on a Z_2 x Z_2' orbifold.
We analyse different N=4 supergravities coupled to six vector multiplets corresponding to low-energy descriptions of the bulk sector of T6/Z2 orientifolds with p-brane in IIB (p odd) and in IIA (p even) superstrings. When fluxes are turned on, a gauging emerges corresponding to some non-semisimple Lie algebra related to nilpotent algebras N_p inside so(6,6), with dimension 15 + (p-3)(9-p). The non-metric axions have Stueckelberg couplings that induce a spontaneous breaking of gauge symmetries. In four cases the gauge algebra is non-abelian with a non-commutative structure of the compactificati…
We study various aspects of orientifold projections of Type IIB closed string theory on Gepner points in different dimensions. The open string sector is introduced, in the usual constructive way, in order to cancel RR charges carried by orientifold planes. Moddings by cyclic permutations of the internal N=2 superconformal blocks as well as by discrete phase symmetries are implemented. Reduction in the number of generations, breaking or enhancements of gauge symmetries and topology changes are shown to be induced by such moddings. Antibranes sector is also considered; in particular we show how …
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 observat…
In this paper, we work out in detail the tadpole cancellation conditions as well as the generalized Green-Schwarz mechanism for type IIB orientifold compactifications with D3- and D7-branes. We find that not only the well-known D3- and D7-tadpole conditions have to be satisfied, but in general also the vanishing of the induced D5-brane charges leads to a non-trivial constraint. In fact, for the case $h^{1,1}_{-} \neq 0$ the latter condition is important for the cancellation of chiral anomalies. We also extend our analysis by including D9- as well as D5-branes and determine the rules for comput…
We present a concrete and consistent procedure to generate one kind of non-perturbative superpotential, including the gaugino condensation corrections and poly-instanton corrections, in type IIB orientifold compactification with four Kahler Moduli. Then we use this kind of superpotential as well as the alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli on a general Calabi-Yau manifold with typical K3-fibred volume form. In our construction, the considered Calabi-Yau threefolds are K3-fibred and admit at least one del Pezzo surface and one W-surface. Searching throu…
We discuss the construction of six- and four-dimensional Type IIB orientifolds with vanishing untwisted RR tadpoles, but generically non-zero twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane systems with zero untwisted RR charge, but non-zero twisted RR charges. We construct explicit models containing branes and antibranes at fixed points of the internal space, or non-BPS branes partially wrapped on it. The models are non-supersymmetric, but are absolutely stable against decay to supersymmetric vacua. For particular values of the compactification radii tachyonic m…
With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and D9-anti-D9 tachyon condensation. A significant complication is that consistent D7-branes in the presence of O7^- planes are generically singular, with singularities locally modeled by the Whitney Umbrella. This invalidates the standard formulae for charges, moduli space and flux lattice dimensions. We infer the correct formulae by comparison to F-theory and derive…
We study moduli stabilization in Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. We consider a Calabi-Yau three-fold with Hodge number $h^{2,1}=50$ and stabilize all axio-dilaton and complex-structure moduli by three-form fluxes. This is a challenging task, especially for large moduli-space dimensions. To address this question we develop an algorithm to generate $10^5$ flux vacua with small flux number $N_{\rm flux}$. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as $N_{\rm flux}\leq \mathc…
We describe the low-energy effective theory of N=1 spontaneously broken supegravity obtained by flux-induced breaking in the presence of n D3 branes. This theory can be obtained by integrating out three massive gravitino multiplets in the hierarchical breaking N=4 to N=3 to N=2 to N=1. This integration also eliminates the IIB complex dilaton. The resulting theory is a no-scale supergravity model, whose moduli are the three chiral multiplets that correspond to the three radii of the three 2-tori in 6-torus, together with the 6n brane coordinates. The U(n) gauge interactions on the branes respec…
We systematically investigate possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis leads to the presence of flat directions at degenerate CP-breaking and -conserving vacua for a generic choice of three-form fluxes, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.
We discuss the four-dimensional N=1 effective actions of single space-time filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N=1 Kaehler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite-dimensional moduli space…
The four-dimensional N=1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kahler potentials are derived for reductions on SU(3) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi-Yau geometry are determined by a reduction of the type IIA and type IIB fermio…
We develop techniques to construct general discrete Wilson lines in four-dimensional N=1 Type IIB orientifolds, their T-dual realization corresponds to branes positioned at the orbifold fixed points. The explicit order two and three Wilson lines along with their tadpole consistency conditions are given for D=4 N=1 Z_6 Type IIB orientifold. The systematic search for all models with general order three Wilson lines leads to a small class of inequivalent models. There are only two inequivalent classes of a potentially phenomenologically interesting model that has a possible SU(3)_{color} x SU(2)_…
Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and periodically correct the Kahler potential. These corrections depend on the NS-NS two form and have to be completed by D-instanton contributions to transform covariantely under symmetries of the type IIB orientifold background. It is shown that generically also the D-instanton superpotential depends on the two-form moduli as well as on the complex dilaton. Thes…
It is often stated in the literature concerning D=4,6 compact Type IIB orientifolds that tadpole cancellation conditions i) uniquely fix the gauge group (up to Wilson lines and/or moving of branes) and ii) are equivalent to gauge anomaly cancellation. We study the relationship between tadpole and anomaly cancellation conditions and qualify both statements. In general the tadpole cancellation conditions imply gauge anomaly cancellation but are stronger than the latter conditions in D=4, N=1 orientifolds. We also find that tadpole cancellation conditions in Z_N D=4,6 compact orientifolds do not …
We consider type IIB flux compactifications on six-dimensional SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We derive the four-dimensional N=1 scalar potential for such compactifications and present one explicit example of a fully stabilized AdS vacuum with large volume and small string coupling. We then discuss cosmological aspects of these compactifications and derive several no-go theorems that forbid dS vacua and slow-roll inflation under certain conditions. We also study concrete examp…
We investigate a class of orientifold models based on tensor products of 18 Ising models. Using the same search criteria as for the comparable case of Gepner model orientifolds we find that there are no three-family standard model configurations with tadpole cancellation. Even if we do not impose the latter requirement, we only find one such configuration in the special case of complex free fermions. In order to allow a comparison with other approaches we enumerate the Hodge numbers of the type-IIB theories we obtain. We provide indications that there are fermionic IIB vacua that are not $Z_2\…
We derive the Lagrangian and the transformation laws of N=4 gauged supergravity coupled to matter multiplets whose sigma-model of the scalars is SU(1,1)/U(1)x SO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effective Lagrangian of the Type IIB string compactified on the T^6/Z_2 orientifold with fluxes turned on and in presence of n D3-branes. The gauge group is T^12 x G where G is the gauge group on the brane and T^12 is the gauge group on the bulk corresponding to the gauged translations of the R-R scalars coming from the R-R four--form. The N=4 bulk sector of this theory can be obtained…
In the present paper, we reexamine the moduli stabilization problem of the Type IIB orientifolds with one complex structure modulus in a modified two-step procedure. The full superpotential including both the 3-form fluxes and the non-perturbative corrections is used to yield a F-term potential. This potential is simplified by using one optimization condition to integrate the dilaton field out. It is shown that having a locally stable supersymmetric Anti-deSitter vacuum is not inevitable for these orientifolds, which depend strongly upon the details of the flux parameters. For those orientifol…
We investigate four-dimensional N=1 Type IIB orientifolds with continuous Wilson lines, and their T-dual realizations as orientifolds with moving branes. When continuous Wilson lines become discrete the gauge symmetry is enhanced and the T-dual orientifold corresponds to branes sitting at the orbifold fixed points. There is a field theoretic analog describing these phenomena as D- and F-flat deformations of the T-dual model, where the branes sit at the origin (original model without Wilson lines) as well as a deformation of the T-dual model where sets of branes sit at the fixed points (the mod…
Compact Type IIB D=4, N=1 orientifolds have certain U(1) sigma model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of $Z_N$ orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singularities and it requires the mixing between twisted and untwisted moduli of the orbifold. As a consequence, the Fayet-Iliopoulos terms which are present for the gauged anomalous U(1)'s of the models get a…
Equipped with concrete examples of Type IIB orientifolds featuring poly-instanton corrections to the superpotential, the effects on moduli stabilization and inflationary cosmology are analyzed. Working in the framework of the LARGE volume scenario, the Kaehler modulus related to the size of the four-cycle supporting the poly-instanton contributes sub-dominantly to the scalar potential. It is shown that this Kaehler modulus gets stabilized and, by displacing it from its minimum, can play the role of an inflaton. Subsequent cosmological implications are discussed and compared to experimental dat…
We determine one-loop string corrections to Kahler potentials in type IIB orientifold compactifications with either N=1 or N=2 supersymmetry, including D-brane moduli, by evaluating string scattering amplitudes.
We systematically analyse globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realisation of SU(5) GUTs with gauge symmetry breaking via U(1)_Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P_{1,1,1,6,9}[18] and of the Quintic P_{1,1,1,1,1}[5], respectively. To define an orientifold proje…
This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes by using a Kaluza-Klein reduction. The Kahler potential, the gauge kinetic functions and the flux-induced superpotential are determined in terms of geometrical data of the Calabi-Yau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin's generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear m…
We address the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions. We present an explicit three-family example with the gauge group (U(4)xU(2)xSU(2)xSU(2))^2x(U(6)xSp(4))^2 and give the particle spectrum and the trilinear superpotential. Emphasizing the new subtleties associated with the introduction of non-Abelian Wilson lines, we show that the Abelian gauge anomalies are cancelled by the Green-Schwarz-type mechanism, and calculate the Fayet-Iliopoulos terms and gauge coupling corrections. The analysis thus sets a stage for further investigations of the p…
We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken {\it à la} Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density $ρ(R)$, or cosmological constant. For SS twists different from Z2 we always find, for both orbifolds and orientifolds, a monotonic $ρ(R)<0$, eventually driving the system to a tachyonic instability. For Z2 twists, orientifold models can have a d…
The massless spectrum of an orientifold of the IIB string theory is computed and shown to be identical to F theory on the Calabi-Yau threefold with $h_{11}=51$ and $h_{21}=3$. Target space duality is also considered in this model.
We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of N=1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also Kahler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications s…
We compute the flux induced tadpole and superpotential in various type IIB $Z_N$ compact orientifolds in order to study moduli stabilization. We find supersymmetric vacua with $g_s < 1$ and describe brane configurations with cancelled tadpoles. In some cases moduli are only partially fixed unless anti D3-branes are included.
We study orbifold compactifications of F-theory which lead to $N=1$ supersymmetry in 6 and 4 spacetime dimensions. These are dual to specific orientifolds of M-theory, and in many cases to orientifolds of type IIB string theory. The equivalences are demonstrated by mapping the orbifolding transformations in the F, M and string theories to each other using dualities. We observe that M and F-theory appear to possess a property similar to discrete torsion in string theory. This is related to an ambiguity recently noted by Polchinski in the orientifold projection for 6-dimensional models. The 4-di…
We study type IIB orientifolds on T^{2d}/Z_N with supersymmetry broken by the compactification. We determine tadpole cancellation conditions including anti-branes and considering different actions for the parity Omega. Using these conditions we then obtain the spectrum of tachyons and massless states. Various examples with N even correspond to type 0B orientifolds.
We study different aspects of the construction of D=4, N=1 type IIB orientifolds based on toroidal Z_N and Z_M x Z_N, D=4 orbifolds. We find that tadpole cancellation conditions are in general more constraining than in six dimensions and that the standard Gimon-Polchinski orientifold projection leads to the impossibility of tadpole cancellations in a number of Z_N orientifolds with even N including Z_4, Z_8, Z_8' and Z_{12}'. We construct D=4, Z_N and Z_N x Z_M orientifolds with different configurations of 9-branes, 5-branes and 7-branes, most of them chiral. Models including the analogue of d…
We consider orientifolds of Calabi-Yau 3-folds in the context of Type IIA and Type IIB superstrings. We show how mirror symmetry can be used to sum up worldsheet instanton contributions to the superpotential for Type IIA superstrings. The relevant worldsheets have the topology of the disc and ${\bf RP^2}$.
