Finiteness of conformal blocks over compact Riemann surfaces

Details Finiteness of conformal blocks over compact Riemann surfaces Finiteness of conformal blocks over compact Riemann surfaces

2002-01-07

arxiv.org/abs/math/0201037v1

Mathematics

Quantum Algebra

Latex2e 16pages

Scientific paper

We study conformal blocks (the space of correlation functions) over compact Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general condition, for instance, $C_2$-finiteness, we prove that conformal blocks are of finite dimensional. This, in particular, shows the finiteness of conformal blocks for many well-known conformal field theories including WZNW model and the minimal model.

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