Disk enumeration on the quintic 3-fold
By R. Pandharipande, Jake Solomon, J. Walcher. 2006
145 citations recorded by the source corpus.
Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Vafa multiple cover formula is used to define virtually enumerative disk invariants. The results may also be viewed as providing a virtual enumeration of real rational curves on the quintic.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/04ef86413e27c692d7729b45e85f73d28df718ad
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Open Gromov-Witten disk invariants in the presence of an anti-symplectic involution (2013, unknown): “This allowed the extension of the definition to a larger class of manifolds and the use of Gromov-Witten techniques for computations leading to a proof of the real mirror symmetry conjecture in [28].”
- Gauged Floer Theory Of Toric Moment Fibers (2010, background): “Secondly, the computation in [44] relates a disk potential defined without markings on the boundary (thus, not the potential that appears in A∞ setting) to a naive potential via a coordinate change that is the same as in the closed case.”
- Open string amplitudes and large order behavior in topological string theory (2006, background): “Most of the explicit results in the open B model refer to disk amplitudes, which have been studied in detail in the local Calabi–Yau (CY) case [7, 5, 35, 50, 51] and more recently in the compact case [70, 65 ].”
- Antisymplectic involution and Floer cohomology (2009, background): “ is that of the fixed point set of an anti-symplectic involution. Actually, the set of real points in Calabi-Yau manifolds plays an important role of homological mirror symmetry conjecture. (See [Wa], [PSW] and [F2]. See also [We] for related topics of real points.) The purpose of the present paper i”