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… 

Figures from this paper

Knot Invariants from Topological Recursion on Augmentation Varieties
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
Abstract loop equations, topological recursion, and applications
We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The
Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds
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
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
Topological Fukaya category and mirror symmetry for punctured surfaces
In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface
M ar 2 01 4 Vertex Operators , C 3 Curve , and Topological Vertex
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
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
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
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)
...
...

References

SHOWING 1-10 OF 42 REFERENCES
A Matrix Model for the Topological String I: Deriving the Matrix Model
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
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
Counting higher genus curves in a Calabi-Yau manifold
The Topological Vertex
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
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
Hodge integrals and Gromov-Witten theory
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these
Zero dimensional Donaldson – Thomas invariants of threefolds
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
Remodeling the B-Model
We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries, including the mirrors of toric manifolds. The formalism is based on
The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
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
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
...
...