论文标题
真空超图的超对称理论的$β$函数：三循环示例
The $β$-function of supersymmetric theories from vacuum supergraphs: a three-loop example
论文作者
论文摘要
我们验证一种方法，该方法允许通过仅计算特殊修改的真空超插图来获得由较高协变量衍生物正规化的超对称理论的$β$功能。在这种方法的帮助下，对于一般的$ξ$ -Gauge构建了这三环$β$ - 功能的一般性$ {\ cal n} = 1 $ supersymmetric量表理论，这是三环$β$ function的一部分。结果是以双重衍生物相对于循环动量的积分的形式编写的。已经证明，所有仪表依赖的术语与一般性声明一致。考虑到Feynman仪表中的结果（前面发现）与标准技术获得的结果相吻合，这一事实证实了通过高度非平凡的多旋转计算的考虑方法的正确性。
We verify a method which allows to obtain the $β$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a part of the three-loop $β$-function depending on the Yukawa couplings is constructed in the general $ξ$-gauge. The result is written in the form of an integral of double total derivatives with respect to the loop momenta. It is demonstrated that all gauge dependent terms cancel each other in agreement with the general statements. Taking into account that the result in the Feynman gauge (found earlier) coincides with the one obtained by the standard technique, this fact confirms the correctness of the considered method by a highly nontrivial multiloop calculation.
