Lectures on Anomalies
Lectures on Anomalies
复制标题
异常讲座
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Bilal
中科院分区：
文献类型：
--
作者：
A. Bilal
这些关于反常现象的讲座是相对独立的，是为那些熟悉量子场理论基础的理论高能物理研究生准备的。在需要时引入更详细的概念。我们开始与几个衍生物的阿贝尔异常：异常的措施，明确计算的三角形费曼图，关系到指数的欧几里德狄拉克运营商。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。本文详细讨论了反常、电流不守恒和作用量不变性之间的关系，特别强调了反常Slavnov-Taylor/Ward恒等式的推导。我们展示了为什么异常总是夜间和本地的。给出了规范群和费米子表示的一般特征，这可能会导致在四维的异常，异常取消的问题进行了讨论，特别是标准模型的经典例子。然后，在第二部分中，我们转向更正式的发展和任意的偶数维。在介绍了一些基本的概念，特别是规范丛和特征类，我们推出的下降方程。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下降方程的特征类在两个维度。计算的异常的指数适当的狄拉克运营商在这些更高的维度概述。最后，我们从适当的指数导出了任意偶数维的规范反常和引力反常，并解释了10维IIB超引力和I型超弦和杂化超弦的ELD理论极限中的反常抵消。
These lectures on anomalies are relatively self-contained and intended for graduate students in theoretical high-energy physics who are familiar with the basics of quantum eld theory. More elaborate concepts are introduced when needed. 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 elds coupled to a chiral fermion. We discuss in detail the relation between anomaly, current non-conservation and non-invariance of the eective action, with special emphasis on the derivation of the anomalous Slavnov-Taylor/Ward identities. We show why anomalies always are nite 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, in a second part, we move to more formal developments and arbitrary even dimensions. After introducing a few basic notions of dierential geometry, in particular the gauge bundle and 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 via the descent equations to characteristic classes in two more dimensions. The computation of the anomalies in terms of the index of an appropriate Dirac operator in these higher dimensions is outlined. 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 the eld theory limits of type I and heterotic superstrings.