Relative periods and open-string integer invariants for a compact Calabi–Yau hypersurface

Jockers, Hans; Soroush, Masoud

doi:10.1016/j.nuclphysb.2009.05.019

Cited by 30 publications

(64 citation statements)

References 30 publications

(91 reference statements)

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“…The geometric structure of open/closed B-model and the associated off-shell superpotential depending on the open and closed string moduli has been studied from the viewpoint of N = 1 special geometry [19,20] for the case of non-compact Calabi-Yau threefolds [15,16]. In [17] (see also [41]), the study of off-shell superpotential was extended to com- In this section, we utilize the method of [17] in general dimensions and explicitly compute the open/closed Picard-Fuchs equation for septic Calabi-Yau fivefold X 7 . Then we will solve the resulting differential system in the vicinity of the Landau-Ginzburg point, and also check the consistency with the on-shell result.…”

Section: Off-shell Formalism Via Relative Periodsmentioning

confidence: 99%

Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

Honma

Manabe

2016

J. High Energ. Phys.

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Abstract:Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of compact CalabiYau manifolds in general dimensions. Our analysis is based on the methods using relative cohomology and generalized hypergeometric system. For the simplest example of compact Calabi-Yau fivefold, we explicitly derive the associated Picard-Fuchs differential equations and compute the quantum corrections in terms of the open and closed flat coordinates. Implications for a kind of open-closed duality are also discussed.

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Section: Off-shell Formalism Via Relative Periodsmentioning

confidence: 99%

Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

Honma

Manabe

2016

J. High Energ. Phys.

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“…Thus, we can interpret the seven-brane superpotential as a special case of the five-brane superpotential, where a description of the five-brane curve Σ in terms of seven-brane flux [F 2 ] = Σ is applicable [80], see also [100,120,121,123,[126][127][128][129] for a similar use of the seven-brane superpotential. 21 It is important to emphasize that the five-brane charge is only locally non-trivial, i.e.…”

Section: The Flux Superpotentialmentioning

confidence: 99%

“…away from the sublocus M P 1 (Σ) defined by (7.34), this embedding implies that the obstructed deformation space of the rational curves (7.35) is identified with the unobstructed moduli space M(Σ). This can be compared to the method presented in [115,120,121,123] where the obstructed deformations of a curve are identified with the unobstructed moduli of an appropriate divisor. For the curves we consider we depict the embedding of the deformation spaces of the rational curves into the moduli space M(Σ) of complete intersection Σ in figure 7.4, where we introduce new open moduliẑ 1 ,ẑ 2 that are functions of the u i .…”

Section: Matching Deformations and Obstructions: Concrete Examplesmentioning

confidence: 99%

“…For D5-branes in compact geometries the superpotential was calculated in [112,114,[116][117][118]122] by deriving and solving inhomogeneous Picard-Fuchs equations. Finally the methods of [110,111] have been extended to compact geometries in [115] and further applied in [120,121,[123][124][125][126][127][128][129].…”

Section: Chaptermentioning

confidence: 99%

“…A technical similar but differently motivated method to obtain toric data and a GKZsystem governing the deformations of toric D5-branes was presented in [109,115,120,121,123,268] and formulated mathematically rigorously in [125].…”

Section: Open-closed Gkz-systems From Blow-up Threefoldsmentioning

confidence: 99%

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Holomorphic couplings in non‐perturbative string compactifications

Klevers

2011

Fortschritte der Physik

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In this review article 1 we present an analysis of several aspects of four-dimensional, nonperturbative N = 1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N = 1 effective action, most prominently the superpotential W . This article is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we perform exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefoldẐ 3 , that is canonically constructed from the original fivebrane and the Calabi-Yau threefold Z 3 via a blow-up. We use the blow-up threefoldẐ 3 to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpretẐ 3 as a flux compactification geometrically dual to the original five-brane by defining an SU (3)-structure onẐ 3 , that is generated dynamically by the five-brane backreaction.

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Superpotentials of D-branes in Calabi-Yau manifolds with several moduli by mirror symmetry and blown-up

Jing

Yang

2022

J. High Energ. Phys.

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We study B-brane superpotentials depending on several closed- and open-moduli on Calabi-Yau hypersurfaces and complete intersections. By blowing up the ambient space along a curve wrapped by B-branes in a Calabi-Yau manifold, we obtain a blow-up new manifold and the period integral satisfying the GKZ-system. Via mirror symmetry to A-model, we calculate the superpotentials and extract Ooguri-Vafa invariants for concrete examples of several open-closed moduli in Calabi-Yau manifolds.

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Relative periods and open-string integer invariants for a compact Calabi–Yau hypersurface

Cited by 30 publications

References 30 publications

Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

Holomorphic couplings in non‐perturbative string compactifications

Superpotentials of D-branes in Calabi-Yau manifolds with several moduli by mirror symmetry and blown-up

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