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How we see a symmetry in a regularized theory

我们如何看待正则化理论中的对称性

基本信息

批准号：
15540262
负责人：
ITO Katsumi
金额：
$ 1.98万
依托单位：
Niigata 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 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540262/
关键词：
Renormalisation Group Supersymmetry Regularisation Gauge Symmetry Anomaly アノマリー繰り込み群

项目摘要

1. Symmetry and exact renormalisation groupA regularization introduced in the exact renormalization group often conflicts with symmetry of a theory. Earlier we have formulated the problem in the Batalin-Vilokovitsky's anti-field formalism and found that the master equation guarantees the presence of symmetry even in a regularized theory. One research during the project clarified how the flow equation respects a symmetry, which appears as a BRS symmetry in our formalism. The result was first obtained for a fermionic system with the chiral symmetry, and recently the similar result was produced for QED. We reported these results in international conferences.2. Supersymmetry on LatticeLattice gauge theory has been a powerful formulation for non-perturbative study. No convincing formulation of a supersymmetric theory on lattice has been known. Earlier, So, Itoh and others found a Grassmannian symmetry for the system of the staggered fermion coupled to link variables with a novel modification of coupling constants, namely the distribution of the coupling constants in the Ichimatsu-pattern. The presence of the symmetry may imply the emergence of supersymmtery in a continuum limit. In order to achieve that, we have to clarify the degrees of freedom both for the fermionic and bosonic part of the theory. Along this line of this thought, we have formulated the staggered fermion respecting the SO(2D) hidden symmetry. Based on that, So and3. Other subjectsWe also abtained some other results on the string field theory and lattice gauge theory. As for the former subject, our result is related to the large gauge symmetry of the SFT and its relation to various solutions that is believed to describe the tachyon condensation. As for the latter, results are obtained on the analogue of Witten's global anomaly and properties of an overlap-type Dirac operator in a gravitational background.

1. 对称与精确重整化群精确重整化群中引入的正则化常常与理论的对称性相冲突。前面我们已经在Batalin-Vilokovitsky的反场形式主义中公式化了这个问题，并且发现主方程即使在正则化理论中也保证了对称性的存在。项目期间的一项研究阐明了流动方程如何尊重对称，这在我们的形式主义中表现为BRS对称。这一结果最初是在具有手性对称性的费米子系统中得到的，最近在QED中也得到了类似的结果。我们在国际会议上报告了这些结果。格点规范理论的超对称已成为非微扰研究的有力表述。目前还没有令人信服的关于晶格的超对称理论的表述。在此之前，So， Itoh等人发现了交错费米子耦合系统的格拉斯曼对称，该系统将变量与耦合常数的一种新的修改联系起来，即耦合常数在一松模式中的分布。对称性的存在可能意味着在连续体极限中出现超对称性。为了达到这个目的，我们必须澄清理论中费米子和玻色子部分的自由度。沿着这条思路，我们制定了尊重SO（2D）隐藏对称的交错费米子。在此基础上，So和3。其他课题在弦场理论和点阵规范理论方面也取得了一些成果。对于前一个主题，我们的结果与SFT的大规范对称性及其与被认为描述速子凝聚的各种解的关系有关。对于后者，给出了引力背景下Witten全球异常的模拟结果和重叠型狄拉克算子的性质。