Verification of new identity for the Green functions in N=1 supersymmetric non-Abelian Yang--Mills theory with the matter fields

TL;DR

This paper proves a new identity for Green functions in N=1 supersymmetric non-Abelian Yang--Mills theory with matter fields, showing it holds at two-loop order due to the factorization of three-loop integrals into total derivatives.

Contribution

It introduces a novel identity for Green functions in supersymmetric gauge theories and demonstrates its validity at two-loop order using higher covariant derivative regularization.

Findings

The new identity relates coefficients in matter superfield vertex functions.

It is valid for non-Abelian Yang--Mills theories with matter fields.

Three-loop integrals factorize into total derivatives, supporting the identity.

Abstract

We investigate a new identity for Green functions using the higher covariant derivative regularization. It relates some coefficients in the vertex function of the matter superfield, in which one of external matter lines is not chiral. The calculation in the first nontrivial order (for the two-loop vertex function) reveals that the new identity is also valid for the non-Abelian Yang--Mills theory with matter fields. The new identity is shown to appear because three-loop integrals, defining the Gell-Mann--Low function are factorized into integrals of total derivatives.