Calabi-Yau Orientifold Compactifications Research Articles

W0_sample = np.random.normal(0,1)?

In this note, we explore the distribution of vacuum expectation values of the superpotential W0 in explicit Type IIB flux compactifications. We show that the distribution can be approximated universally across geometries by a two-dimensional Gaussian with a model-dependent standard deviation. We identify this behaviour in 20 Calabi-Yau orientifold compactifications with between two and five complex structure moduli by constructing a total of O(107) flux vacua. We observe a characteristic scaling behaviour of the width σ of our distributions with respect to the D3-charge contributions Nflux from fluxes which can be approximated by σ∼Nflux. This W0 distribution implies that locating small values of |W0| as a preferred regime associated with classes of string theory solutions typically featuring hierarchies, simplifies to the basic statement of finding small Euclidean norms of normally distributed values. We also identify small modifications to this Gaussian behaviour in our samples, which might be seen as indications for the breakdown of the continuous flux approximation commonly used in the context of statistical analyses of the flux landscape.

Cobordism and bubbles of anything in the string landscape

We study bubble of nothing decays and their reverse processes, the creation of vacua through ‘bubbles of something’, in models of the Universe based on string theory. From the four-dimensional perspective, the corresponding gravitational instantons contain an end-of-the-world (ETW) boundary or brane, realized by the internal manifold shrinking to zero size. The existence of such ETW branes is predicted by the Cobordism Conjecture. We develop the 4d EFT description of such boundaries at three levels: first, by generalizing the Witten bubble through an additional defect. Second, by replacing the compact S1 with a Calabi-Yau orientifold and allowing it to shrink and disappear through a postulated defect. Third, we describe an ETW brane construction for type IIB Calabi-Yau orientifold compactifications with O3/O7 planes through an appropriate additional O5 orientifolding. Our 4d EFT formalism allows us to compute the decay/creation rates for bubbles of anything depending on two parameters: the size of the relevant defect and its tension a.k.a. the induced (generalized) deficit angle.

Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions

In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion of the mass matrix for F-term vacua in four-dimensional mathcal{N} = 1 supergravity theories and then specialize to type IIB Calabi-Yau orientifold compactifications in the presence of geometric and non-geometric fluxes. F-term vacua in this setting are in general AdS4 vacua for which we compute the conformal dimensions of operators dual to the scalar fields. For the mirror-dual of the DGKT construction we find that one-loop corrections to the complex-structure moduli space lead to real-valued conformal dimensions — only when ignoring these corrections we recover the integer values previously reported in the literature. For an example of a flux configurations more general than the DGKT mirror we also obtain non-integer conformal dimensions. Furthermore, we argue that stabilizing the axio-dilaton and complex-structure moduli in asymptotic regions of moduli space by fluxes implies that at least one of the corresponding mass eigenvalues diverges.

Systematics of type IIB moduli stabilisation with odd axions

Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms (B2, C2) in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D mathcal{N} = 1 F-term scalar potentials at higher orders in the α′ and gs expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of (α′)3 corrections to the Kähler potential. By studying a partially SL(2, ℤ)-completed form of the Kähler potential, we derive the exact no-scale breaking effects at the closed string 1-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the F-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.

The tadpole conjecture at large complex-structure

The tadpole conjecture by Bena, Blåbäck, Graña and Lüst effectively states that for string-theory compactifications with a large number of complex-structure moduli, not all of these moduli can be stabilized by fluxes. In this note we study this conjecture in the large complex-structure regime using statistical data obtained by Demirtas, Long, McAllister and Stillman for the Kreuzer-Skarke list. We estimate a lower bound on the flux number in type IIB Calabi-Yau orientifold compactifications at large complex-structure and for large h2,1, and our results support the tadpole conjecture in this regime.

Systematics of the \u03b1\u2032 expansion in F-theory

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate (α′)even corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that (α′)odd effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from (α′)3 effects, modulo potential logarithmic corrections.

On \u03b1\u2032-effects from D-branes in 4d mathcal{N} = 1

In this work we study type IIB Calabi-Yau orientifold compactifications in the presence of space-time filling D7-branes and O7-planes. In particular, we conclude that α′2gs-corrections to their DBI actions lead to a modification of the four-dimensional mathcal{N} = 1 Kähler potential and coordinates. We focus on the one-modulus case of the geometric background i.e. h1,1 = 1 where we find that the α′2gs-correction is of topological nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau orientifold which is wrapped by the D7-branes and O7-plane. This is in agreement with our previous F-theory analysis and provides further evidence for a potential breaking of the no-scale structure at order α′2gs. Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss α′-corrections from other Dp-branes.

D-brane instantons on non-Spin cycles

Abstract We show that non-Spin cycles in type IIB Calabi-Yau orientifold compactifications with vanishing B field naturally support orientifold-invariant D-brane instantons. These instantons, associated to the holomorphic cotangent bundle of the non-Spin cycle, can lead to non-perturbative corrections to the superpotential.

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.

Large volume axionic Swiss cheese inflation

Continuing with the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's, arXiv: 0707.0105 [hep-th], Nucl. Phys. B, in press], after inclusion of perturbative and non-perturbative α ′ corrections to the Kähler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of slow roll axionic inflation in the large volume limit of Swiss cheese Calabi–Yau orientifold compactifications of type IIB string theory. We also include one- and two-loop corrections to the Kähler potential but find the same to be subdominant to the (perturbative and non-perturbative) α ′ corrections. The NS–NS axions provide a flat direction for slow roll inflation to proceed from a saddle point to the nearest dS minimum.

Flux compactifications and generalized geometries**This is an abridged version of Physics Reports, M Graña, ‘Flux compactifications in string theory: A comprehensive review’ 423 91–158, Copyright (2006), reprinted with permission from Elsevier.

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi–Yau and Calabi–Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

The effective action of D‐branes in Calabi‐Yau orientifold compactifications

AbstractIn this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.

D-terms and F-terms from D7-brane fluxes

Using a Kaluza–Klein reduction of the fermionic part of the D-brane action we compute D- and F-terms of the N = 1 effective action for generic Calabi–Yau orientifold compactifications in the presence of a space–time filling D7-brane. We include non-trivial background fluxes for the D7-brane U ( 1 ) field strength on the internal four-cycle wrapped by the brane. First the four-dimensional fermionic spectrum arising from the D7-brane is derived and then the D- and F-terms are obtained by computing appropriate couplings of these fermionic fields. For specific examples we examine the resulting flux-induced scalar potentials and comment on their relevance in string cosmology.