# Ward identities from recursion formulas for correlation functions in conformal field theory

## Alexander Zuevsky

Address: Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague

E-mail: zuevsky@yahoo.com

Abstract: 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.

AMSclassification: primary 30F10; secondary 17B69, 81T40.

Keywords: conformal field theory, conformal blocks, recursion formulas, vertex algebras.

DOI: 10.5817/AM2015-5-347