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)人们普遍认为规范理论的大N极限是用所谓的Eguchi-Kawai简化模型来描述的。我们考虑了与晶格上的手征规范理论相对应的简化模型，并系统地研究了该模型中可能存在的规范异常。在这项研究中，我们首次针对多种规范场配置提出了一种规范组 U(N) 基本表示中的费米子异常计算方法。 (2)近年来，基于Ginsparg-Wilson关系，我们提出了格子手性规范理论，基于这一发展，Wess-Zumino-Witten。我们发现，由于使用 Ginsparg-Wilson 关系，Wess-Zumino-Witten 的拓扑性质。 (3) 众所周知，二维玻色子化可以通过使用反常现象来解释，然而，在这个论证中，一个看似不相关的术语可以被局部反术语删除。文献中对这一点的理解存在混乱；我们根据局域性论证澄清了这种混乱的根源（4）我们指出马约拉纳和格的表述存在根本性的困难。 Majorana-Weyl 费米子，取决于时空的维度，我们认为，这个困难与 Witten 的全局规范异常密切相关。 (5) 我们从格子公式的角度重新考虑了规范理论的量子化。基于 Ginsparg-Wilson 关系，我们证明了这种系统的一致表述通常是不可能的。我们还论证了异常被消除的理论的可能含义。 (6) 我们构建了四维超对称 Wess-Zumino 模型的晶格公式，该模型保留了精确的 U(1)R 对称性。