Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

Knapp, Johanna; Scheidegger, Emanuel

doi:10.4310/atmp.2009.v13.n4.a3

Cited by 27 publications

(68 citation statements)

References 67 publications

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“…We consider the Calabi-Yau threefold, which arises as the mirror of the family of degree eight hypersurfaces in the weighted projective space, WP [29,30] in agreement with our results.…”

Section: Open/closed Picard-fuchs Differential Equations and Flat Coosupporting

confidence: 76%

“…[29,30]. There the relevant D5-branes wrap the holomorphic two cycles, C ± , which are respectively given in the ambient weighted projective space by…”

Section: The Calabi-yau and D-brane Geometrymentioning

confidence: 99%

“…Following this recipe similar computations have been carried out successfully for other one-parameter Calabi-Yau geometries in refs. [29,30].…”

Section: Introductionmentioning

confidence: 99%

“…[24,25], we propose in this work an analog method to derive Picard- We apply these novel techniques to D5-branes in Calabi-Yau threefolds, which are related to the geometries discussed in the context of domain wall tensions in refs. [27,29,30].…”

Section: Introductionmentioning

confidence: 99%

“…Finally, as a bonus and as a highly non-trivial consistency check we reproduce for our two examples the domain wall tension computed in refs. [27,29,30] by evaluating the calculated effective superpotential at its critical points.…”

Section: Introductionmentioning

confidence: 99%

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Effective Superpotentials for Compact D5-Brane Calabi-Yau Geometries

Jockers

Soroush

2009

Commun. Math. Phys.

189

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For compact Calabi-Yau geometries with D5-branes we study N = 1 effective super- nates. By evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature. Finally we extract orbifold disk invariants from the superpotentials, which, up to overall numerical normalizations, correspond to orbifold disk Gromov-Witten invariants in the mirror geometry.

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“…We consider the Calabi-Yau threefold, which arises as the mirror of the family of degree eight hypersurfaces in the weighted projective space, WP [29,30] in agreement with our results.…”

Section: Open/closed Picard-fuchs Differential Equations and Flat Coosupporting

confidence: 76%

“…[29,30]. There the relevant D5-branes wrap the holomorphic two cycles, C ± , which are respectively given in the ambient weighted projective space by…”

Section: The Calabi-yau and D-brane Geometrymentioning

confidence: 99%

“…Following this recipe similar computations have been carried out successfully for other one-parameter Calabi-Yau geometries in refs. [29,30].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Effective Superpotentials for Compact D5-Brane Calabi-Yau Geometries

Jockers

Soroush

2009

Commun. Math. Phys.

189

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The volume conjecture and topological strings

Dijkgraaf

Fuji²

2009

Fortschritte der Physik

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In this paper, we discuss a relation between Jones-Witten theory of knot invariants and topological open string theory on the basis of the volume conjecture. We find a similar Hamiltonian structure for both theories, and interpret the AJ conjecture as the D-module structure for a D-brane partition function. In order to verify our claim, we compute the free energy for the annulus contributions in the topological string using the Chern-Simons matrix model, and find that it coincides with the Reidemeister torsion in the case of the figure-eight knot complement and the SnapPea census manifold m009.The hyperbolic three-manifold M is given bywhere Γ is a torsion-free and discrete subgroup of P SL(2; C) with the action (2.2).The volume of an ideal tetrahedron T αβγ is computed directly by using the metric (2.1) [33].The function Λ(θ) is called the Lobachevsky function. The volume formula can also be rewritten in terms of the Bloch-Wigner function D(z)(2.9)The gluing condition along each edge imposes constraints on the face angles of the ideal tetrahedra.(2.10)Furthermore, we should also consider the gluing condition for the boundary of the knot complement. In order to realize the torus as a boundary, the face angles must satisfy the completeness conditions along the meridian and the longitude.Mostow's rigidity theorem [34] implies that these conditions are solved uniquely with Im z i > 0 for all i. By summing all volumes for the ideal tetrahedra, we are able to determine the hyperbolic volume uniquely for each hyperbolic three-manifold.

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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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Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces

Cited by 27 publications

References 67 publications

Effective Superpotentials for Compact D5-Brane Calabi-Yau Geometries

Effective Superpotentials for Compact D5-Brane Calabi-Yau Geometries

The volume conjecture and topological strings

Holomorphic couplings in non‐perturbative string compactifications

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