# Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence - Mathematical Physics

Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We propose an asymptotic expansion formula for matrix integrals, includingoscillatory terms derivatives of theta-functions to all orders. This formulais heuristically derived from the analogy between matrix integrals, and formalmatrix models combinatorics of discrete surfaces, after summing over fillingfractions. The whole oscillatory series can also be resummed into a singletheta function. We also remark that the coefficients of the theta derivatives,are the same as those which appear in holomorphic anomaly equations in stringtheory, i.e. they are related to degeneracies of Riemann surfaces. Moreover,the expansion presented here, happens to be independent of the choice of abackground filling fraction.

Author: ** Bertrand Eynard SPhT**

Source: https://arxiv.org/