期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 3, 页码 -出版社
SPRINGER
DOI: 10.1088/1126-6708/2009/03/003
关键词
Matrix Models; Differential and Algebraic Geometry; Topological Strings
资金
- Enigma European network [MRT-CT-2004-5652]
- Enrage European network [ANR-05-BLAN-0029-01]
- European Science Foundation [MRTN-CT-2004-005616]
- French and Japaneese governments
- Quebec government with the FQRNT
We propose an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders. This formula is heuristically derived from the analogy between matrix integrals, and formal matrix models (combinatorics of discrete surfaces), after summing over filling fractions. The whole oscillatory series can also be resummed into a single theta function. We also remark that the coefficients of the theta derivatives, are the same as those which appear in holomorphic anomaly equations in string theory, i.e. they are related to degeneracies of Riemann surfaces. Moreover, the expansion presented here, happens to be independent of the choice of a background filling fraction.
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