Opening Mirror Symmetry on the Quintic

By J. Walcher. 2006

136 citations recorded by the source corpus.

Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. We hypothesize that the tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We further check the conjecture by reproducing the first few instanton numbers by a localization computation directly in the A-model, and verifying Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7ffc25786eb930b32965c15bec94fc38e6edfe54

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In Geometry and Topology

1. Marcos Mariño
2. A. Klemm
3. V. Bouchard
4. Sara Pasquetti
5. B. Eynard
6. K. Fukaya
7. Pavel Putrov
8. H. Ohta

In Nuclear and High Energy Physics

1. Marcos Mariño
2. V. Bouchard
3. Sara Pasquetti
4. A. Klemm
5. C. Vafa
6. Pavel Putrov
7. B. Eynard
8. Yong-Geun Oh

Citations in the corpus

• Antisymplectic involution and Floer cohomology (2009, background): “ifolds 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 p”
• Remodeling the B-Model (2007, methodology): “Note that disk amplitudes ending on the real quintic inside the quintic threefold have also been calculated [44], using a generalization of the Abel-Jacobi map [27].”
• 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].”
• Counting pseudo-holomorphic discs in Calabi-Yau 3 fold (2009, unknown): “on 8.2, it seems likely that we can reproduce the invariants of Solomon and Welschinger [22]. The superpotential we defined in this paper is also likely to be related to the numbers studied by Walcher [21]. (For such a purpose we need to include flat bundle on L. In fact in [21] it seems that several ”