arXiv 0802.06342008-02-05hep-th

异常现象讲座

Lectures on Anomalies

Adel Bilal

备注：: 108 pages, 10 figures

摘要：

这些关于反常现象的讲座是相对独立的，是为熟悉量子场论基础的研究生准备的。我们从阿贝尔反常的几个推导开始：反常的测度变换，三角形费曼图的显式计算，与欧几里德狄拉克算子指数的关系。通过计算三个非阿贝尔规范场与手征费米子耦合的反常三角图，导出手征（非阿贝尔）规范场反常。详细讨论了反常、电流不守恒和有效作用量不变性之间的关系，特别强调了反常斯拉夫诺夫-泰勒/沃德恒等式的推导。我们表明为什么异常总是有限的和本地的。给出了可能导致四维反常的规范群和费米子表象的一般特征，并讨论了反常抵消问题，特别是标准模型的经典例子。然后，我们转向更正式的发展和任意的偶数维度。在介绍了微分几何的一些基本概念，特别是特征类，我们推导出下降方程。我们证明了Wess-Zumino的一致性条件，并表明相关的异常对应于BRST上同调鬼数1。我们讨论为什么以及如何异常相关的特征类在两个维度和概述其计算方面的指数适当的狄拉克算子。最后，我们从适当的指数导出了任意偶数维的规范和引力异常，并解释了10维IIB超引力和I型超弦和杂合超弦中的异常抵消。

英文摘要：

These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the measure, explicit computation of the triangle Feynman diagram, relation to the index of the Euclidean Dirac operator. The chiral (non-abelian) gauge anomaly is derived by evaluating the anomalous triangle diagram with three non-abelian gauge fields coupled to a chiral fermion. We discuss in detail the relation between anomaly, current non-conservation and non-invariance of the effective action, with special emphasis on the derivation of the anomalous Slavnov-Taylor/Ward identities. We show why anomalies always are finite and local. A general characterization is given of gauge groups and fermion representations which may lead to anomalies in four dimensions, and the issue of anomaly cancellation is discussed, in particular the classical example of the standard model. Then, we move to more formal developments and arbitrary even dimensions. After introducing a few basic notions of differential geometry, in particular characteristic classes, we derive the descent equations. We prove the Wess-Zumino consistency condition and show that relevant anomalies correspond to BRST cohomologies at ghost number one. We discuss why and how anomalies are related to characteristic classes in two more dimensions and outline their computation in terms of the index of an appropriate Dirac operator. Finally we derive the gauge and gravitational anomalies in arbitrary even dimensions from the appropriate index and explain the anomaly cancellations in ten-dimensional IIB supergravity and in type I and heterotic superstrings.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文