The four-loop $\beta$-function from vacuum supergraphs and the NSVZ relation for ${\cal N}=1$ SQED regularized by higher derivatives

Abstract

In ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives we obtain the four-loop beta function using a method based on calculating vacuum supergraphs. For this purpose we use a special C++ program which obtain contributions to the $\beta$-function from supergraphs without external legs in the form of integrals of double total derivatives. After that the result was compared with the three-loop anomalous dimension calculated earlier. We explicitly check the NSVZ relation in this order.