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Ward identities from recursion formulas for correlation functions in conformal field theory. (English) Zbl 1389.30151
Summary: A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find $$n$$-point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg and free fermionic vertex operator algebras are supplied.
##### MSC:
 30F10 Compact Riemann surfaces and uniformization 17B69 Vertex operators; vertex operator algebras and related structures 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
##### Keywords:
conformal field theory; conformal blocks; vertex algebras
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