Verifying a new identity for Green's functions of the $N=1$ supersymmetric non-Abelian Yang–Mills theory with matter fields

We use the higher covariant derivative regularization to investigate a new identity for Green's functions. It relates certain coefficients of the matter superfield vertex function for which one of the external matter legs is not chiral. Calculations in the first nontrivial order (for the two-loop vertex function) demonstrate that the new identity also holds in the non-Abelian Yang–Mills theory with matter fields. We demonstrate that the new identity follows because the three-loop integrals determining the Gell-Mann–Low function are integrals of total derivatives.