Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-10-23
J.Geom.Phys.61:1181-1202,2011
Physics
High Energy Physics
High Energy Physics - Theory
40 pages, 11 figures, added reference and additional results on background independence
Scientific paper
10.1016/j.geomphys.2010.11.012
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.
Eynard Bertrand
Marino Marcos
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