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Erschienen in:
2016 | OriginalPaper | Buchkapitel
6. Intersection Numbers of Curves
verfasst von : Edouard Brézin, Shinobu Hikami
Erschienen in: Random Matrix Theory with an External Source
Verlag: Springer Singapore
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Abstract
Witten (Two dimensional gravity and intersection theory on moduli space, surveys in differential geometry 1, 243–310, 1991, [134]) conjectured that a generating function of the intersection numbers of the moduli space of curves on a Riemann surface with marked points, is a solution of the KdV hierarchy. Kontsevich (Commun Math Phys 147:1–23, 1992, [89]) has proved this conjecture with the use of an Airy matrix model. In addition it has been realized that matrix models of this type are examples of an exact closed/open strings duality (Gaiotto and Rastelli, JHEP 07:053, 2005, [63]).