# Topological recursion and mirror curves

@article{Bouchard2011TopologicalRA, title={Topological recursion and mirror curves}, author={Vincent Bouchard and Piotr Sułkowski}, journal={arXiv: High Energy Physics - Theory}, year={2011} }

We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov-Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the "remodeling conjecture" to the full free energies, including the constant contributions. In the process we study how the pair of pants…

## 33 Citations

### Knot Invariants from Topological Recursion on Augmentation Varieties

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Using the duality between Wilson loop expectation values of SU(N) Chern–Simons theory on S3 and topological open-string amplitudes on the local mirror of the resolved conifold, we study knots on S3…

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### Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds

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- 2020

Abstract
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### Topological Fukaya category and mirror symmetry for punctured surfaces

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Abstract In this article, we prove the conjecture that Kodaira-Spencer theory for the topological vertex is a free fermion theory. By dividing the C curve into core and asymptotic regions and using…

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### All-genus open-closed mirror symmetry for affine toric Calabi�Yau 3-orbifolds

- MathematicsAlgebraic Geometry
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The Remodeling Conjecture proposed by Bouchard-Klemm-Marino-Pasquetti [arXiv:0709.1453, arXiv:0807.0597] relates all genus open and closed Gromov-Witten invariants of a semi-projective toric…

### On the remodeling conjecture for toric Calabi-Yau 3-orbifolds

- MathematicsJournal of the American Mathematical Society
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The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants)…

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