AI 中文总结
研究任意可重整 \({\cal N}=1\) 超对称理论，通过高阶协变导数正则化单个规范耦合，计算物质超场反常维度三圈贡献及规范 \(β\) 函数四圈贡献，构建“最小”重整化方案并研究其性质。
AI 中文摘要
对于一个通过高阶协变导数正则化单个规范耦合的任意可重整 \({\cal N}=1\) 超对称理论，我们针对多种重整化方案计算了物质超场反常维度的三圈贡献，该贡献与汤川耦合的六次幂成正比。接着，考虑到在高阶协变导数辅以对数的最小减法的情况下，NSVZ 关系在所有阶都成立，我们计算了规范 \(β\) 函数的相应四圈贡献并研究其方案依赖性。特别地，我们构建了所谓的“最小”重整化方案，在超对称给出的规范和汤川 \(β\) 函数的精确方程仍然有效的条件下，该方案的重整化群函数具有尽可能简单的形式。
英文摘要
For an arbitrary renormalizable ${\cal N}=1$ supersymmetric theory with a single gauge coupling regularized by higher covariant derivatives we calculate the three-loop contribution to the anomalous dimension of the matter superfields proportional to the sixth powers of Yukawa couplings for a wide class of renormalization prescriptions. Next, taking into account that in the case of using the higher covariant derivatives supplemented by minimal subtractions of logarithms the NSVZ relation is valid in all orders, we calculate the corresponding four-loop contribution to the gauge $β$-function and investigate its scheme dependence. In particular, we construct the so-called ``minimal'' renormalization prescription for which the renormalization group functions have the simplest possible form provided that the exact equations for the gauge and Yukawa $β$-functions following from supersymmetry remain valid.
Comments25 pages, 2 figures
