On the geometry of operator mixing in massless QCD-like theories
On the geometry of operator mixing in massless QCD-like theories
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无质量类 QCD 理论中算子混合的几何
DOI：
10.1140/epjc/s10052-021-09543-5
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
M. Bochicchio
中科院分区：
文献类型：
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作者：
M. Bochicchio
我们重新审视无质量类 QCD 理论中的算子混合。特别是，我们解决了确定在哪些条件下存在重整化方案的问题，其中坐标表示中的重整化混合矩阵可对角化到所有扰动阶。作为关键的一步，我们提供了重整化的微分几何解释，使我们能够将庞加莱-杜拉克定理应用于上述问题：我们将重整化方案的变化解释为（形式）全纯规范变换，作为与富克斯奇点的（形式）亚纯连接，以及与反常维数矩阵和 beta 函数的威尔逊线。根据庞加莱-杜拉克定理，如果矩阵的特征值（按非递增顺序）满足 k 正整数的非共振条件，则存在重正化方案，其中单循环精确于所有微扰阶。另外如果 是可对角化的， 也是可对角化的，并且混合本质上简化为可乘法可重整化的情况。我们还通过庞加莱-杜拉克定理对剩余的算子混合情况进行分类。
We revisit the operator mixing in massless QCD-like theories. In particular, we address the problem of determining under which conditions a renormalization scheme exists where the renormalized mixing matrix in the coordinate representation,, is diagonalizable to all perturbative orders. As a key step, we provide a differential-geometric interpretation of renormalization that allows us to apply the Poincaré-Dulac theorem to the problem above: We interpret a change of renormalization scheme as a (formal) holomorphic gauge transformation,as a (formal) meromorphic connection with a Fuchsian singularity at, andas a Wilson line, withthe matrix of the anomalous dimensions andthe beta function. As a consequence of the Poincaré-Dulac theorem, if the eigenvaluesof the matrix, in nonincreasing order, satisfy the nonresonant conditionforandka positive integer, then a renormalization scheme exists whereis one-loop exact to all perturbative orders. If in additionis diagonalizable,is diagonalizable as well, and the mixing reduces essentially to the multiplicatively renormalizable case. We also classify the remaining cases of operator mixing by the Poincaré–Dulac theorem.