 Then for formula_8 the Knizhnik–Zamolodchikov equations read

The Knizhnik–Zamolodchikov equations result from 
the Sugawara construction of the Virasoro algebra from the affine Lie algebra.More specifically, they result from applying the identity 

to the affine primary field formula_11 in a correlation function of affine primary fields.In this context, only the terms formula_12 are non-vanishing.