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

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Abstract

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(1–2):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 \({K_{\mathbb{P}^2}}\) (Graber-Zaslow, Contemp Math 310:107–121, 2002), (ii) an outer brane at arbitrary framing in the resolved conifold \({\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)}\) (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 \({K_{\mathbb{P}^2}}\) (Brini, Open topological strings and integrable hierarchies: Remodeling the A-model. http://arxiv.org/abs/1102.0281 [hep-th], 2011).

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, 2990 Broadway, New York, NY, 10027, USA

    Bohan Fang & Chiu-Chu Melissa Liu

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  1. Bohan Fang
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  2. Chiu-Chu Melissa Liu
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Correspondence to Bohan Fang.

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Communicated by N. A. Nekrasov

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Fang, B., Liu, CC.M. Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds. Commun. Math. Phys. 323, 285–328 (2013). https://doi.org/10.1007/s00220-013-1771-5

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