# 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

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

- Mathematics
- 2014

This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of…

Nahm sums, quiver A-polynomials and topological recursion

- MathematicsJournal of High Energy Physics
- 2020

Abstract
We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and…

M ar 2 01 4 Vertex Operators , C 3 Curve , and Topological Vertex

- Mathematics
- 2014

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…

Painlevé 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas

- Mathematics
- 2017

The goal of this article is to prove that the determinantal formulas of the Painlevé 2 system identify with the correlation functions computed from the topological recursion on their spectral curve…

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

- MathematicsAlgebraic Geometry
- 2020

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
- 2019

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)…

Challenges of β-deformation

- Mathematics
- 2012

We briefly review problems arising in the study of the beta deformation, which turns out to be the most difficult element in a number of modern problems: the deviation of β from unity is connected…

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

- Mathematics
- 2013

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…

Integrability in non-perturbative QFT

- Mathematics
- 2013

Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional…

## References

SHOWING 1-10 OF 42 REFERENCES

A Matrix Model for the Topological String I: Deriving the Matrix Model

- Mathematics
- 2010

We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi–Yau threefolds. This demonstrates, in accord with the BKMP “remodeling the B-model”…

Hurwitz numbers, matrix models and enumerative geometry

- Mathematics
- 2007

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric…

The Topological Vertex

- Mathematics, Physics
- 2005

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the…

A Matrix Model for the Topological String II: The Spectral Curve and Mirror Geometry

- Mathematics
- 2010

In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi–Yau manifold. Here, we compute the spectral curve of our…

Zero dimensional Donaldson – Thomas invariants of threefolds

- Mathematics
- 2009

Ever since the pioneer work of Donaldson and Thomas on Yang–Mills theory over Calabi–Yau threefolds [5, 13], people have been searching for their roles in the study of Calabi–Yau geometry and their…

The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers

- Mathematics
- 2009

Author(s): Eynard, Bertrand; Mulase, Motohico; Safnuk, Brad | Abstract: We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial…

Open string amplitudes and large order behavior in topological string theory

- Mathematics
- 2008

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open…

All order asymptotic expansion of large partitions

- Mathematics
- 2008

The generating function which counts partitions with the Plancherel measure (and its q-deformed version) can be rewritten as a matrix integral, which allows one to compute its asymptotic expansion to…

Topological Open Strings on Orbifolds

- Mathematics
- 2010

We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the…

Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants

- Mathematics
- 2005

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the…