A holomorphic and background independent partition function for matrix models and topological strings

Abstract

We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi-Yau threefolds.

40 pages, 11 figures, added reference and additional results on background independence

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• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
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• Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
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• Duality Constraints on String Theory: Instantons and spectral networks
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• Wronskians, dualities and FZZT-Cardy branes