A matrix model for the topological string I: Deriving the matrix model

Bertrand Eynard; Amir-Kian Kashani-Poor; Olivier Marchal

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arXiv · 1003.1737

A matrix model for the topological string I: Deriving the matrix model

Bertrand Eynard·Amir-Kian Kashani-Poor·Olivier Marchal

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Abstract

We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of any toric Calabi-Yau 3-fold can be computed in terms of the spectral invariants of a spectral curve. Moreover, it proves that the generating function of Gromov-Witten invariants is a tau function for an integrable hierarchy. In a follow-up paper, we will explicitly construct the spectral curve of our matrix model and argue that it equals the mirror curve of the toric Calabi-Yau manifold.

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Bertrand Eynard, Amir-Kian Kashani-Poor, Olivier Marchal. 2010-03-17. A matrix model for the topological string I: Deriving the matrix model. https://arxiv.org/abs/1003.1737

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