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

TL;DR

This paper introduces a nonperturbative, holomorphic, and background-independent partition function for matrix models and topological strings, incorporating all instanton effects and satisfying key mathematical properties.

Contribution

It constructs a nonperturbative partition function that is modular, background independent, and satisfies the Hirota equation, providing a new completion for topological string theory.

Findings

Partition function includes all multi-instanton corrections.

It is modular and background independent, transforming as a twisted fermion.

Obeys Hirota equation and offers a nonperturbative topological string completion.

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.