For \({\cal N} = 1\) supersymmetric Yang—Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization group β-function, defined in terms of the renormalized coupling constant, is valid. These schemes are related with each other by finite renormalizations forming a one-parameter commutative subgroup of general renormalization group transformations. The analogy between the exact β-function in \({\cal N} = 1\) supersymmetric Yang-Mills theory without matter and the β-function of quantum chromodynamics in the C-scheme is discussed.

中文翻译：

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Abelian和非Abelian $$ {\ cal N} = 1 $$ N = 1超对称量规模型中的精确β函数及其与C方案中QCDβ函数的类比

对于\（{\ cal N} = 1 \）超对称Yang-Mills理论，无论如何，证明存在一类重整化方案，其中精确的Novikov，Shifman，Vainshtein和Zakharov（NSVZ）公式用于重整化根据重新归一化的耦合常数定义的β组函数是有效的。这些方案通过有限的重新规范化而相互关联，从而形成了常规重新规范化组转换的一个参数可交换子组。讨论了\（{\ cal N} = 1 \）超对称Yang-Mills理论中没有物质的精确β函数与C方案中量子色动力学的β函数之间的类比。