The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories

Abstract

We discuss why the Slavnov higher covariant derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allowed to demonstrate that the $\beta$-function in these theories is given by integrals of double total derivatives and to construct the NSVZ renormalization prescription in all loops. It was also used for deriving the non-renormalization theorem for the triple gauge-ghost vertices. With the help of this theorem the exact NSVZ $\beta$-function was rewritten in a new form, which revealed its perturbative origin. Moreover, in the case of using the higher covariant derivative regularization it is possible to construct a method for obtaining the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories, which simplifies the calculations in a great extent. This method is illustrated by an explicit two-loop calculation made in the general $\xi$-gauge.

15 pages, 1 figure, minor corrections, to appear in the special volume of Proceedings of the Steklov Institute of Mathematics in honor of Prof. A.A.Slavnov on his 80-th anniversary

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Cited by in corpus (9)

• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
• Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Finiteness of the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories: the two-loop verification
• The four-loop $\beta$-function from vacuum supergraphs and the NSVZ relation for $\mathcal{N}=1$ SQED regularized by higher derivatives
• The $\beta$-function of supersymmetric theories from vacuum supergraphs: a three-loop example
• Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace