Study on chiral symmetry in lattice gauge theory

格子规范理论中的手性对称性研究

基本信息

批准号：
15540250
负责人：
SUZUKI Hiroshi
金额：
$ 1.98万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

(1)It is commonly believed that the large N limit of gauge theories is described by so-called Eguchi-Kawai's reduced model. We considered a reduced model which corresponds to chiral gauge theories on the lattice and systematically studied possible gauge anomalies in this model at the first time. In this study, we presented, for a wide class of gauge field configurations, a calculational method of anomalies for fermions in the fundamental representation of gauge group U(N). Next, we calculated anomalies in a large N limit for general gauge group representations. (2)In recent years, a formulation of chiral gauge theories on the lattice on the basis of the Ginsparg-Wilson relation. We formulate, based on this development, the Wess-Zumino-Witten action on the lattice and analyzed geometrical properties of the formulation. We found, as a consequence of the use of Ginsparg-Wilson relation, that topological properties of the Wess-Zumino-Witten action are ensured even on the lattice. (3) It ha … More s been known that two-dimensional bosonization can be interpreted by using the anomaly. In this argument, however, a seemingly irrelevant term which may be removed by a local counter term plays a crucial role. There was confusion in the literature on an understanding on this point ; we clarified the origin of this confusion based on the locality argument. (4) We pointed out that there is a fundamental difficulty concerning lattice formulation of the Majorana and Majorana-Weyl fermions, depending on the dimensionality of spacetime. We argued that, this difficulty is closely related to Witten's global gauge anomaly. (5) We reconsidered a quantization of gauge theories with local gauge anomalies from a view point, of a lattice formulation based on the Ginsparg-Wilson relation. We showed that a consistent formulation of such systems is generally impossible. We also argued a possible implication for theories in which the anomaly is cancelled by the Green-Schwarz mechanism. (6) We constructed a lattice formulation of four dimensional supersymmetric Wess-Zumino model which preserves the exact. U(1)R symmetry. Less

（1）通常认为，量规理论的较大n极限是由所谓的Eguchi-Kawai的还原模型描述的。我们考虑了一个简化的模型，该模型对应于晶格上的手性量规理论，并首次在该模型中系统地研究了可能的量规态。在这项研究中，我们介绍了广泛的量规场构型，这是量规u（n）基本表示中fermions的一种计算方法。接下来，我们计算了通用量规组表示的大N限制的异常。（2）近年来，根据金斯帕格 - 威尔逊关系，在晶格上的手性规理论公式。我们根据这种发展制定了对晶格的Wess-Zumino-witten作用，并分析了公式的几何特性。我们发现，由于使用了金斯帕格·威尔森（Ginsparg-Wilson）的关系，即使在晶格上，也确保了韦斯 - 祖米诺（Wess-Zumino-witten）行动的拓扑特性。（3）众所周知，可以使用异常来解释二维琼脂化。然而，在这个论点中，一个看似无关紧要的术语可以被当地的反术语删除至关重要的作用。关于这一点的理解，文献中存在混乱。我们根据当地论点阐明了这种混乱的起源。（4）我们指出，根据时空的尺寸，关于Majorana和Majorana-Weyl Fermions的晶格公式存在一个基本困难。我们认为，这个困难与维滕的全球仪表异常密切相关。（5）我们从一个基于金斯帕格·威尔森（Ginsparg-Wilson）关系的晶格公式的局部规范对量规理论的量化理论进行了重新考虑。我们还争辩说，对绿色 - 奇瓦兹机制取消异常的理论可能有可能的含义。（6）我们构建了一个四维超对称Wess-Zumino模型的晶格公式，该模型保留了确切的晶格。 U（1）R对称性。较少的