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

2010/03/08 by Bertrand Eynard, Eynard, Bertrand, Amir-Kian Kashani-Poor +3
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1003.1737

1+34 pages; v2: references added

openalex publication_date 2010/03/08 · arxiv created 2010/03/17 · arxiv updated 2010/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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