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

Abstract

AbstractIn $${{{\mathcal {N}}}}=1$$ N = 1 SQED with $$N_f$$ 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 $$\beta $$ β -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.