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

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

2011-03-03

arxiv.org/abs/1103.0693v2

Mathematics

Symplectic Geometry

39 pages, 11 figures

Scientific paper

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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