Abstract

We review some recent results of the studies of quantum corrections in supersymmetric theories derived using Slavnov’s higher covariant derivative regularization. In particular, we demonstrate that the \(\beta\)-function of \(\mathcal{N}=1\) supersymmetric theories is related to the anomalous dimensions of matter superfields by the NSVZ relation if the theory is regularized by higher covariant derivatives and the renormalization group functions are defined in terms of the bare couplings, because the corresponding loop corrections are given by integrals of double total derivatives in the momentum space. For the standard renormalization-group functions, we show that an all-loop NSVZ renormalization scheme is given by the HD\(\,+\,\)MSL renormalization prescription when the higher covariant derivative regularization is supplemented by minimal subtractions of logarithms. Applications of these results to the precise calculations in various supersymmetric theories are briefly described.

中文翻译：

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高等协变导数正则化超对称理论中量子修正的结构和精确结果

摘要

我们回顾了使用斯拉夫诺夫的高协变导数正则化导出的超对称理论中量子校正研究的一些最新结果。特别是，我们证明，如果该理论通过更高协变正则化，则\(\mathcal{N}=1\)超对称理论的\(\beta\)函数通过 NSVZ 关系与物质超场的反常维度相关导数和重整化群函数是根据裸耦合定义的，因为相应的环路修正是由动量空间中的二重全导数的积分给出的。对于标准重整化群函数，我们表明，当较高协变导数正则化由最小对数减法补充时，全循环 NSVZ 重整化方案由 HD \(\,+\,\) MSL 重整化规定给出。简要描述了这些结果在各种超对称理论中精确计算的应用。