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Determinant bundles and Virasoro algebras. (English) Zbl 0665.17010
This paper studies the interplay between the following objects: (1) The Virasoro algebra and its highest weight representations. (2). The moduli space of curves. (3) Determinant bundles. (4) Conformal field theory.
For example, the Virasoro algebra acts by infinitesimal deformations on the moduli space and on the determinant bundle. Representations of the Virasoro algebra give rise to D-modules on the moduli space which can be interpreted as differential equations for correlation functions in conformal field theory.
Reviewer: A.N.Pressley

17B65 Infinite-dimensional Lie (super)algebras
14H10 Families, moduli of curves (algebraic)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
Full Text: DOI
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