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Construction of supersymmetric field theories by Ichimatsu-patterned lattice and application to nonperturbative renormalization group

一松型晶格构建超对称场论及其在非微扰重正化群中的应用

基本信息

批准号：
17540242
负责人：
SO Hiroto
金额：
$ 1.54万
依托单位：
Ehime University (2006-2007)Niigata University (2005)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

The purpose of this project is to construct regularized field theories in order to understand a unified (supersymmetric) mode of fundamental particle physics and to obtain a new idea on symmetry realized in regularized field theories.Since our fundamental particle physics is dominated by “gauge principle", its regularized version must be also gauged. The lattice gauge theory is a most suitable approach but the usual cubic lattice is less symmetry than our world.An Ichimatsu-patterned lattice has a substructure inside the normal cubic lattice. It is characteristic on account of fermionic degrees of freedom. We have made it clear that fermi fields on a Ichimatsu-patterned lattice are described by SO(2D) not SO(D) where D is space-time dimension. This surprising fact leads us to understand a doubling phenomena that fermionic degrees are 2^<(2D)/2> not 2^<D/2> in a unit lattice. Supersymmetric theories have a balance between bosonic and fermionic degree of freedom, and the counterpart for gauge freedom remains as an open problem.Why is the realization of supersymmetry difficult unlike gauge symmetry? One of reasons is the path integral measure of fermi fields. The simplest case is a 0-dimensional case and we have studied the global anomaly under the existence of Majorana fermions. The consequence is that the consistent theory enforces us even number of Majorana fermions in the theory such as Witten's anomaly. On the other hand, how can we set a Majorana fermion on lattice? According to an approach of Luescher for a chiral symmetry, we have tried a Majorana condition. To our regret, the result is not satisfied with chiral Yukawa couplings. Therefore, we need to get systematical approach of symmetry in regularized filed theories. The quantum master equation can describe the realization necessarily and sufficiently. This approach can apply to a system with external gravitational fields.

本项目的目的是为了理解基本粒子物理的统一（超对称）模式，并获得在正则化场论中实现的关于对称性的新想法，而构造正则化场论。由于我们的基本粒子物理是由“规范原理”支配的，因此它的正则化版本也必须被规范。格点规范理论是一种最合适的方法，但通常的立方格点的对称性不如我们的世界，一松格点在立方格点内部有一个子结构。这是费米子自由度的特征。我们已经清楚地表明，一松格点上的费米场是用SO（2D）描述的，而不是SO（D），其中D是时空维。这一令人惊讶的事实使我们理解了一种加倍现象，即在单位晶格中，费米子度是2^<（2D）/2>而不是2^<D/2>。超对称理论在玻色子自由度和费米子自由度之间取得了平衡，而规范自由度的对应物仍然是一个悬而未决的问题。为什么超对称的实现比规范对称困难？原因之一是费米场的路径积分测度。最简单的情形是0维情形，我们研究了Majorana费米子存在下的整体反常。结果是自洽理论强制我们在维滕反常等理论中有偶数个马约拉纳费米子。另一方面，我们如何在格点上设置一个马约拉纳费米子？根据Luescher关于手征对称性的方法，我们尝试了Majorana条件。遗憾的是，对于手征Yukawa耦合，结果并不令人满意。因此，我们需要对正则化场论中的对称性进行系统的研究。量子主方程可以充分、必要地描述这种实现。这种方法可以应用于具有外部引力场的系统。