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.
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机译：在保形场理论中，对Zhu递归过程的保形块公式进行了介绍，该保形块公式允许根据较低的相关函数找到$ n $点函数。然后定义了作用于VOA模块张量积的Zhu归约算子。通过这些算子，我们表明Zhu归约过程为顶点算子代数的保形块生成了Ward身份的显式形式。提供了Heisenberg和自由费米离子顶点算子代数的Ward身份的明确示例。
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