Type IIB Orientifolds Research Articles

A note on poly-instanton effects in type IIB orientifolds on Calabi-Yau threefolds

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.

The [formula omitted] effective actions of D-branes in Type IIA and IIB orientifolds

We discuss the four-dimensional N = 1 effective actions of single space–time filling D p -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 Kähler 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 of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kähler two-forms of Calabi–Yau manifolds. These elegantly combine in the N = 1 Kähler potential, which reduces after applying mirror symmetry to the results previously determined for space–time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kähler potentials of Type IIB D-branes.

Fluxed instantons and moduli stabilization in type IIB orientifolds andFtheory

We study the superpotential induced by Euclidean D3-brane instantons carrying instanton flux, with special emphasis on its significance for the stabilisation of Kahler moduli and Neveu-Schwarz axions in Type IIB orientifolds. Quite generally, once a chiral observable sector is included in the compactification, arising on intersecting D7-branes with world-volume flux, resulting charged instanton zero modes prevent a class of instantons from participating in moduli stabilisation. We show that instanton flux on Euclidean D3-branes can remove these extra zero modes and helps in reinstating full moduli stabilisation within a geometric regime. We comment also on the F-theoretic description of this effect of alleviating the general tension between moduli stabilisation and chirality. In addition we propose an alternative solution to this problem based on dressing the instantons with charged matter fields which is unique to F-theory and cannot be realised in the weak coupling limit.

Quantum corrections to heterotic moduli potentials

In a recent paper, we derived the leading alpha' corrections to the Kahler potentials for moduli in (0,2) heterotic compactifications. In the same spirit as the LARGE volume stabilization scenario for type IIB orientifolds, we examine whether these quantum corrections, together with a combination of tree-level and non-perturbative superpotentials, are sufficient to stabilize the overall volume modulus at large values. This is not a priori obvious, since the corrections we found are of a lower order than those used in the type IIB setting. Nevertheless, we find that stabilizing the volume at (exponentially) large values may be possible (under certain conditions) in these heterotic backgrounds.

Lectures on F-theory compactifications and model building

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to type IIB orientifolds, the geometry of elliptic fibrations and the emergence of gauge groups, matter and Yukawa couplings. As a suitable framework for the construction of compact F-theory vacua we describe a special class of Weierstrass models called Tate models, whose local properties are captured by the spectral cover construction. Armed with this technology we proceed with a survey of F-theory grand unified theory (GUT) models, aiming at an overview of basic conceptual and phenomenological aspects, in particular in connection with GUT breaking via hypercharge flux.

Basics of F‐theory from the Type IIB perspective

AbstractThese short lecture notes provide an introduction to some basic notions of F‐theory with some special emphasis on its relation to Type IIB orientifolds with O7/O3‐planes.

D-instanton and polyinstanton effects from type I’ D0-brane loops

We study non-perturbative D(-1)-instanton corrections to quartic gauge and curvature couplings in 8d type IIB orientifolds, in terms of a one-loop computation of BPS D0-branes in T-dual type I' models. The complete perturbative and non-perturbative results are determined by the BPS multiplicities of perturbative open strings and D0-brane bound states in the 9d type I' theory. Its modular properties admit a geometric interpretation by lifting to Horava-Witten theory. We use the type I' viewpoint to motivate a proper interpretation of 8d and 4d polyinstanton effects, consistent with heterotic - type II orientifold duality.

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 zeromode 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

FLUX PARAMETER SPACES IN TYPE II VACUA

We study the flux parameter spaces for semirealistic supersymmetric Pati–Salam models in the AdS vacua on Type IIA orientifold and realistic supersymmetric Pati–Salam models in the Minkowski vacua on Type IIB orientifold. Because the fluxes can be very large, we show explicitly that there indeed exists a huge number of semirealistic Type IIA and realistic Type IIB flux models. In the Type IIA flux models, in the very large flux limit, the theory can become weakly coupled and the AdS vacua can approach to the Minkowski vacua. In a series of realistic Type IIB flux models, at the string scale, the gauge symmetry can be broken down to the Standard Model gauge symmetry, the gauge coupling unification can be achieved naturally, all the extra chiral exotic particles can be decoupled, and the observed Standard Model fermion masses and mixings can be obtained as well. In particular, the real parts of the dilaton, Kähler moduli, and the unified gauge coupling are independent of the very large fluxes. The very large fluxes only affect the real and/or imaginary parts of the complex structure moduli, and/or the imaginary parts of the dilaton and Kähler moduli. However, these semirealistic Type IIA and realistic Type IIB flux models cannot be populated in the string landscape.

The generalized Green-Schwarz mechanism for type IIB orientifolds with D3- and D7-branes

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 computing the chiral spectrum of the combined system.

Chern class identities from tadpole matching in type IIB and F-theory

In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and of certain related surfaces. We present the physical argument leading to the identity, and a mathematical derivation of a Chern class identity which confirms it, after taking into account singularities of the relevant loci. This identity of Chern classes holds in arbitrary dimension, and for varieties that are not necessarily Calabi-Yau. Singularities are essential in both the physics and the mathematics arguments: the tadpole relation may be interpreted as an identity involving stringy invariants of a singular hypersurface, and corrections for the presence of pinch-points. The mathematical discussion is streamlined by the use of Chern-Schwartz-MacPherson classes of singular varieties. We also show how the main identity may be obtained by applying `Verdier specialization' to suitable constructible functions.

Issues ofSU(5) Grand Unification in Type IIB Orientifolds

In this talk we review some of the recent developements on realising grand unified theories in string theory. We explain that F-theory GUTs combine all the model building advantages of the heterotic string with a natural framework for advancing the hierarchy between the GUT and the Planck scale to a basic string model building concept. In the second more technical part some issues for the weakly couple Type IIB orientifold regime are discussed in more detail.

Algebras and non-geometric flux vacua

In this work we classify the subalgebras satisfied by non-geometric Q-fluxes in type IIB orientifolds on T6/(2 × 2) with three moduli (S, T, U). We find that there are five subalgebras compatible with the symmetries, each one leading to a characteristic flux-induced superpotential. Working in the 4-dimensional effective supergravity we obtain families of supersymmetric AdS4 vacua with all moduli stabilized at small string coupling gs. Our results are mostly analytic thanks to a judicious parametrization of the non-geometric, RR and NSNS fluxes. We are also able to leave the flux-induced C4 and C8RR tadpoles as free variables, thereby enabling us to study which values are allowed for each Q-subalgebra. Another novel outcome is the appearance of multiple vacua for special sets of fluxes. However, they generically have gs > 1 unless the net number of O3/D3 or O7/D7 sources needed to cancel the tadpoles is large. We also discuss briefly the issues of axionic shift symmetries and cancellation of Freed-Witten anomalies.

No-scale supersymmetry breaking vacua and soft terms with torsion

We analyze the conditions to have no-scale supersymmetry breaking solutions of type IIA and IIB supergravity compactified on manifolds of SU(3)-structure. The supersymmetry is spontaneously broken by the intrinsic torsion of the internal space. For type IIB orientifolds with O9 and O5-planes the mass of the gravitino is governed by the torsion class 1, and the breaking is mediated through F-terms associated to descendants of the original = 2 hypermultiplets. For type IIA orientifolds with O6-planes we find two families of solutions, depending on whether the breaking is mediated exclusively by hypermultiplets or by a mixture of hypermultiplets and vector multiplets, the latter case corresponding to a class of Scherk-Schwarz compactifications not dual to any geometric IIB setup. We compute the geometrically induced μ-terms for D5, D6 and D9-branes on twisted tori, and discuss the patterns of soft-terms which arise for pure moduli mediation in each type of breaking. As for D3 and D7-branes in presence of 3-form fluxes, the effective scalar potential turns out to possess interesting phenomenological properties.

Lifting D-instanton zero modes by recombination and background fluxes

We study the conditions under which D-brane instantons in Type II orientifold compactifications generate a non-perturbative superpotential. If the instanton is non-invariant under the orientifold action, it carries four instead of the two Goldstone fermions required for superpotential contributions. Unless these are lifted, the instanton can at best generate higher fermionic F-terms of Beasley-Witten type. We analyse two strategies to lift the additional zero modes. First we discuss the process of instantonic brane recombination in Type IIA orientifolds. We show that in some cases charge invariance of the measure enforces the presence of further zero modes which, unlike the Goldstinos, cannot be absorbed. In other cases, the instanton exhibits reparameterisation zero modes after recombination and a superpotential is generated if these are lifted by suitable closed or open string couplings. In the second part of the paper we address lifting the extra Goldstinos of D3-brane instantons by supersymmetric three-form background fluxes in Type IIB orientifolds. This requires non-trivial gauge flux on the instanton. Only if the part of the fermionic action linear in the gauge flux survives the orientifold projection can the extra Goldstinos be lifted.

ON THE MODIFIED KKLT PROCEDURE: A CASE STUDY FOR THE P11169[18] MODEL

We probe the existence of supersymmetric vacua of the type IIB orientifold of the elliptic Calabi–Yau space P11169[18] where generically two complex structure moduli zi, the dilaton τ and the two Kähler moduli Ti are stabilized by fluxes and gaugino condensates. The usual KKLT procedure, which integrates out the complex structure moduli and the dilaton, actually has to be modified, such that one keeps the dependence on τ. We derive explicitly the resulting effective superpotential W eff (τ) for the dilaton for various flux combinations. As this is actually a nonholomorphic quantity one must properly work with the G-function. The remaining SUSY equations for τ and the Ti can be resolved explicitly.

Moduli stabilization in non-geometric backgrounds

Type II orientifolds based on Landau–Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kähler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as anti-de Sitter vacua. This construction provides the first string vacuum with all moduli frozen and leading to a 4D Minkowski background.

Orientifolds of Gepner models

We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a configuration of rational branes must satisfy for consistency (tadpole cancellation and rank constraints) and spacetime supersymmetry. For certain cases, including Type IIB orientifolds of the quintic and a two parameter model, one can find all solutions in this class. Depending on the parity, the number of vacua can be large, of the order of 10^{10}-10^{13}. For other models, it is hard to find all solutions but special solutions can be found -- some of them are chiral. We also make comparison with the large volume regime and obtain a perfect match. Through this study, we find a number of new features of Type II orientifolds, including the structure of moduli space and the change in the type of O-planes under navigation through non-geometric phases.

Moduli stabilization in type IIB orientifolds (II)

We discuss general properties of moduli stabilization in KKLT scenarios in type IIB orientifold compactifications X 6 . In particular, we find conditions for the Kähler 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 × Z M -orientifolds X 6 with h ( 2 , 1 ) ( X 6 ) = 0 for a KKLT scenario. This concerns Z 3 , Z 7 , Z 3 × Z 3 , Z 4 × Z 4 , Z 6 × Z 6 and Z 2 × Z 6 ′ -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kähler moduli associated to the odd cohomology H − ( 1 , 1 ) ( X 6 ) . In the second part of this work we discuss the moduli stabilization of resolved type IIB Z N - or Z N × Z M -orbifold/orientifold compactifications. As examples for the resolved Z 6 and Z 2 × Z 4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.

Moduli stabilization in type IIB orientifolds (I)

We discuss flux quantization and moduli stabilization in toroidal type IIB Z N - or Z N × 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.