Factorization of integrals defining the two-loop beta-function for the general renormalizable N=1 SYM theory, regularized by the higher covariant derivatives, into integrals of double total derivatives

TL;DR

This paper demonstrates that two-loop beta-function integrals in N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, can be expressed as integrals of double total derivatives, simplifying calculations and confirming the NSVZ beta-function.

Contribution

It shows that two-loop integrals can be reduced to one-loop integrals using double total derivatives and delta-functions, aligning with the exact NSVZ beta-function.

Findings

Two-loop integrals are expressed as double total derivatives.

Delta-functions enable reduction to one-loop integrals.

Results agree with the NSVZ beta-function.

Abstract

The integrals defining the two-loop beta-function for the general renormalizable N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, are investigated. It is shown that they are given by integrals of double total derivatives. These integrals are not equal to zero due to appearing of delta-functions. These delta-functions allow to reduce the two-loop integrals to one-loop integrals, which can be easily calculated. The result agrees with the exact NSVZ beta-function and calculations made by different methods.