Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
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- 作者：Bohan Fang (1)
Chiu-Chu Melissa Liu (1) - 刊名：Communications in Mathematical Physics
- 出版年：2013
- 出版时间：October 2013
- 年：2013
- 卷：323
- 期：1
- 页码：285-328
- 全文大小：740KB
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Chiu-Chu Melissa Liu (1)
1. Department of Mathematics, Columbia University, 2990 Broadway, New York, NY, 10027, USA
文摘
We present a proof of the mirror conjecture of Aganagic and Vafa (Mirror Symmetry, D-Branes and Counting Holomorphic Discs. http://arxiv.org/abs/hep-th/0012041v1, 2000) and Aganagic et?al. (Z Naturforsch A 57(1-):128, 2002) 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 ${K_{\mathbb{P}^2}}$ K P 2 (Graber-Zaslow, Contemp Math 310:107-21, 2002), (ii) an outer brane at arbitrary framing in the resolved conifold ${\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)}$ O P 1 ( - 1 ) ⊿O P 1 ( - 1 ) (Zhou, Open string invariants and mirror curve of the resolved conifold. http://arxiv.org/abs/1001.0447v1 [math.AG], 2010), and (iii) an outer brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Brini, Open topological strings and integrable hierarchies: Remodeling the A-model. http://arxiv.org/abs/1102.0281 [hep-th], 2011).