Invertible Cohomological Field Theories and Weil–petersson Volumes
نویسنده
چکیده
Abstract. 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 Hodge 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.
منابع مشابه
Quantum Cohomology of a Product
0. Introduction 0.1. Quantum cohomology. Quantum cohomology of a projective algebraic manifold V is a formal deformation of its cohomology ring. Parameters of this deformation are coordinates on the space H * (V), and the structure constants are the third derivatives of a formal series Φ V (potential, or free energy) whose coefficients count the number of parametrized rational curves on V with ...
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