Publication : t08/026

Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence

Eynard B. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Abstract:
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.
Année de publication : 2009
Revue : JHEP 0903 003 (2009)
DOI : 10.1088/1126-6708/2009/03/003
Preprint : arXiv:0802.1788
Langue : Anglais

Fichier(s) à télécharger :
  • 1126-6708_2009_03_003.pdf
  • publi.pdf

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