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Annales Henri Poincaré

, Volume 17, Issue 10, pp 2741–2781 | Cite as

Matrix Models from Operators and Topological Strings, 2

  • Rinat KashaevEmail author
  • Marcos Mariño
  • Szabolcs Zakany
Article

Abstract

The quantization of mirror curves to toric Calabi–Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbative realization of topological string theory on these backgrounds. In this paper, we find an explicit form for the integral kernel of the trace class operator in the case of local \({{\mathbb{P}}^1 \times {\mathbb{P}}^1}\), in terms of Faddeev’s quantum dilogarithm. The matrix model associated to this integral kernel is an \({O(2)}\) model, which generalizes the ABJ(M) matrix model. We find its exact planar limit, and we provide detailed evidence that its \({1/N}\) expansion captures the all genus topological string free energy on local \({{\mathbb{P}}^1 \times {\mathbb{P}}^1}\).

Keywords

Matrix Model Topological String ABJM Theory Trace Class Operator Hooft Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Rinat Kashaev
    • 1
    Email author
  • Marcos Mariño
    • 1
    • 2
  • Szabolcs Zakany
    • 2
  1. 1.Section de MathématiquesUniversité de GenèveGenèveSwitzerland
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGenèveSwitzerland

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