Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

2011/03/31 by Bohan Fang, Chiu-Chu Melissa Liu · 1 citation
Mathematics · Physics and Astronomy · #math.SG #hep-th #math.AG

paper · pdf · doi:10.1007/s00220-013-1771-5

published as Commun. Math. Phys. 323 (2013), 285-328 · 39 pages, 11 figures

arxiv created 2012/03/26 · arxiv updated 2015/05/27

Abstract

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).

Citations

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Open-String Gromov-Witten Invariants: Calculations and a Mirror "Theorem"
• Open String Invariants and Mirror Curve of the Resolved Conifold
• Open Topological Strings and Integrable Hierarchies: Remodeling the A-Model

Cited by

• Open-closed Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks