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

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

2010-03-08

arxiv.org/abs/1003.1737v2

Physics

High Energy Physics

High Energy Physics - Theory

1+34 pages; v2: references added

Scientific paper

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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