期刊
ANNALES DE L INSTITUT FOURIER
卷 50, 期 2, 页码 519-+出版社
ANNALES DE L INSTITUT FOURIER
DOI: 10.5802/aif.1764
关键词
moduli spaces; cohomological field theories; Weil-Petersson volumes
类别
We show that the generating function for the higher Weil-Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten's free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a very large phase space, correlation functions on which include Wedge integrals studied by C. Faber and R. Pandharipande. From this formula we derive an asymptotical expression for the Weil-Petersson volume as conjectured by C. Itzykson. We also discuss a topological interpretation of the genus expansion formula of Itzykson-Zuber, as well as a related bialgebra acting upon quantum cohomology as a complex version of the classical path groupoid.
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