One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

Abstract

We consider a general non-Abelian renormalizable $\mathcal{N}=1$ supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop $\beta$-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop $\beta$-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.

arXiv comment17 pages, 4 figures

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• Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories and the NSVZ relation
• The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
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• On supersymmetric gauge theories with higher derivatives and nonlocal terms in the matter sector
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• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace