Investigation on supersymmetric Pauli-Villars regularization for supersymmetric standard models

Frolov和Slavnov提出的广义Pauli-Villars方法提出了手性规范理论及其超对称扩展的手性对称正则化和规范对称正则化的可能性。通过对他们的方法进行分析，从一般的不专门化到特定的模型，我们重构了一种广义的Pauli-Villlars正则化方法，阐明了该方法的有效性。我们进一步尝试将其推广到超对称手性规范理论。我们的调查结果可以概括如下：广义Pauli-Villars方法可以应用于具有一般规范群的理论。当费米子属于无异常表示时，理论可以在不影响手性和规范对称性的情况下进行正则化。这个结果是非平凡的，因为一般认为在正则化手性费米子时，手性对称性不能与规范对称性相一致。对于含有异常费米子的理论，这种方法不能完全起作用，规范电流中会出现奇异项。正则化自动产生横向真空偏振张量。此外，在费米子数和共形电流中出现的异常具有规范不变形式。广义Pauli-Villars方法与Fujikawa的协变正则化方法密切相关，因为它明显地保留了规范对称性。对于超对称的手性规范理论，也可以构造出明显的规范协变和超对称的正则化。它再现了协变测量异常。结果表明，该方法为各种异常提供了一种更简单的计算方案。我们还没有成功地实现广义Pauli-Villars方法的超对称，这需要进一步的研究。目前还不完全清楚这种概括是否可能。我们通过分析协变正则化规范电流的结构得到的结果，有力地表明了将广义Pauli-Villars正则化推广到超对称手性规范理论的可能性。少

The generalized Pauli-Villars method proposed by Frolov and Slavnov suggests the possibility of chiral symmetric as well as gauge symmetric reguralization for chiral gauge theories and their supersymmetric extensions. By analyzing their method from general setting which is not specialized to a particular model, we reconstructed a generalized Pauli-Villlars regularization method, clarifying the validity of this method. We further tried to extend it to supersymmetric chiral gauge theories. The outcome of our investigation can be summarized as follows :1.The generalized Pauli-Villars method can be applied to theories with general gauge group. When fermions belong to an anomaly free representation, the theory can be reguralized without affecting both chiral and gauge symmetries. This result is highly nontrivial because it is generally believed that chiral symmetry can not be consistent with gauge symmetry in regularizing chiral fermions. For theories with anomalous fermion contents, this m … More ethod does not work completely and there arise singular terms in the gauge currents.2.The regularization yields automatically the transverse vacuum polarization tensor. Furthermore, the anomalies appearing in fermion numbers and conformal currents possess gauge invarinat forms.3.The generalized Pauli-Villars method turns out to be intimately related to Fujikawa's covariant regularization method since it preserves manifestly the gauge symmetry.4.A regularization which is manifestly gauge-covariant and supersymmetric can also be formulated for super-symmetric chiral gauge theories. It reproduces covariant gauge anomalies. It turned out that our method provids a simpler computational scheme for various anomalies.We have not succeeded in supersymmetrizing the generalized Pauli-Villars method, which should be investigated further. At present, it is not completely clear whether such generalization is possible or not. Our consequences obtained so far by analyzing the structure of covariantly regularized gauge currents strongly suggest the possibility of extending the generalized Pauli-Villars regularization to supersymmetric chiral gauge theories. Less