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

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Eynard, Bertrand^3,4  Marino, Marcos^1,2 

[1] Univ Geneva, Sect Math, CH-1211 Geneva, Switzerland

[2] Univ Geneva, Dept Phys Theor, CH-1211 Geneva, Switzerland

[3] CEA, Inst Phys Theor, IPhT, F-91191 Gif Sur Yvette, France

[4] CNRS, URA 2306, F-91191 Gif Sur Yvette, France

关键词: Partition function;    Spectral curve;    Matrix models;    1/N expansion;    Hirota equation;   

DOI  :  10.1016/j.geomphys.2010.11.012

来源: Elsevier

【 摘 要 】

We study various properties of a nonperturbative partition function which can be associated with 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 3-folds. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free