Three-loop renormalization of the Wess–Zumino–Witten model

The covariant background field method and the 't Hooft–Veltman prescription for dimensional regularization are used to calculate the three-loop $1/\varepsilon$-counterterm in the two-dimensional Wess–Zumino–Witten model. The perturbative result for the three-loop $\beta$-function is found to be in agreement with the non-perturbative one obtained for this model by means of the conformal field theory technique.