Two-loop renormalization of the Faddeev--Popov ghosts in ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives

TL;DR

This paper calculates the two-loop anomalous dimensions of Faddeev--Popov ghosts in ${ m extbf{N=1}}$ supersymmetric gauge theories using higher derivative regularization, revealing scheme dependence and nonlinear renormalization effects.

Contribution

It provides the first two-loop calculation of ghost anomalous dimensions in ${ m extbf{N=1}}$ supersymmetric gauge theories with higher derivative regularization, accounting for nonlinear renormalization.

Findings

Two-loop anomalous dimension in terms of bare coupling constant.

Dependence of ghost anomalous dimension on subtraction scheme.

Nonlinear renormalization of the quantum gauge superfield.

Abstract

For the general renormalizable ${\cal N}=1$ supersymmetric gauge theory we investigate renormalization of the Faddeev--Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension defined in terms of the bare coupling constant in the general $\xi$-gauge. It is demonstrated that for doing this calculation one should take into account that the quantum gauge superfield is renormalized in a nonlinear way. Next, we obtain the two-loop anomalous dimension of the Faddeev--Popov ghosts defined in terms of the renormalized coupling constant and examine its dependence on the subtraction scheme.