Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces

Knapp, Johanna; Scheidegger, Emanuel

doi:10.48550/arxiv.0805.1013

Cited by 26 publications

(71 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The holomorphic curves needed for the computation of (2.12) were representatives of the second algebraic Chern classes of these matrix factorizations. A similar strategy was pursued in [20,21] for the other one-parameter hypersurfaces.…”

Section: Extensionsmentioning

confidence: 99%

“…The selection principle for the matrix factorizations in [2,20] was a conjectural mirror relation to the Lagrangian submanifolds given as real slices of the corresponding Amodel geometry. (In [21], a different scheme was used, see [35] for a possible extension to multi-parameter models. )…”

Section: Extensionsmentioning

confidence: 99%

“…The quantity (1.1), which depends on discrete open string, and continuous closed string moduli, has a classical mathematical meaning in the B-model [2], as well as an enumerative interpretation in the A-model [19]. Following the quintic, a handful of examples have now been worked out [20,21]. Progress on the relation to the framework of [16] has also been made, see [22,23,24,25].…”

mentioning

confidence: 99%

“…Of those ten, four are geometrically realized by hypersurfaces in weighted projective space, and the relevant D-brane geometries were identified in A-and B-model in [1,2,20,21]. (The integrality can then be a formal consequence of [26].)…”

mentioning

confidence: 99%

See 3 more Smart Citations

Calculations for mirror symmetry with D-branes

Walcher

2009

J. High Energy Phys.

View full text Add to dashboard Cite

We study normal functions capturing D-brane superpotentials on several one-and twoparameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D-branes. A 4-d domain wall which is obtained in one region of closed string moduli space from wrapping a four-chain interpolating between two Lagrangian submanifolds is, for other values of the parameters, represented by a disk ending on a single Lagrangian.

show abstract

Section: Extensionsmentioning

confidence: 99%

Section: Extensionsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Calculations for mirror symmetry with D-branes

Walcher

2009

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…Recently, however, there has been significant progress in computing disk instantons in the context of compact Calabi-Yau geometries. In a series of remarkable papers [8,9,10,11], the authors compute disk instanton invariants for involution branes in compact Calabi-Yau geometries. Physically, the computed disk instanton generating functions capture the domain wall tension between supersymmetric vacua of two distinct D-brane configurations.…”

Section: Introductionmentioning

confidence: 99%

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

Jockers

Soroush

2009

Nuclear Physics B

View full text Add to dashboard Cite

The volume conjecture and topological strings

Dijkgraaf

Fuji²

2009

Fortschritte der Physik

View full text Add to dashboard Cite

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.

show abstract

Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces

Cited by 26 publications

References 61 publications

Calculations for mirror symmetry with D-branes

Calculations for mirror symmetry with D-branes

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

The volume conjecture and topological strings

Contact Info

Product

Resources

About