Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
Bohan Fang, Chiu-Chu Melissa Liu
TL;DR
This paper proves the mirror conjecture for disk enumeration in all smooth semi-projective toric Calabi-Yau 3-folds, unifying and extending previous results for various specific cases and brane configurations.
Contribution
It provides a comprehensive proof of the mirror conjecture for disk counts in toric Calabi-Yau 3-folds, covering all smooth semi-projective cases and various brane framings.
Findings
Confirmed the mirror conjecture for inner and outer branes at arbitrary framing.
Unified previous results on disk enumeration in specific toric Calabi-Yau geometries.
Extended the validity of the conjecture to all smooth semi-projective cases.
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]).
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