Matrix models for topological strings: exact results in the planar limit

2018/10/18 by Szabolcs Zakany, Zakany, Szabolcs
Computer Science · Mathematics · Physics and Astronomy · #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1810.08608

46 pages, 2 figures

arxiv created 2018/10/18 · openalex publication_date 2018/10/18 · arxiv updated 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the large N expansion of a family of matrix models related to topological strings on toric Calabi-Yau threefolds. These matrix models compute spectral observables of underlying operators obtained by quantizing the mirror curves. They have the form of a deformed O(2) matrix model, with a specific non-polynomial potential involving the Faddeev quantum dilogarithm. Their planar limit is studied using a particular conformal mapping depending on two parameters, from which several universal results can be obtained. As expected, the spectral curves controlling the planar limit of the matrix models are the mirror curves themselves, which in our cases have genus 1. Our results encompass all those toric geometries with genus 1 mirror where an explicit one-cut matrix integral is known: local P², local F₀, local F₂, and degenerations of the resolved C³/Z₅, the resolved C³/Z₆ and the resolved Y^3,0 geometries amongst others.

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