The Physics of Large Extra Dimension

本研究项目取得的主要成果如下：1.尝试在规范-希格斯统一模型的基础上构建一个现实的模型。首席研究人员曾与Hatanaka和Inami合作提出了一个方案，利用规范-Higgs统一方案自然地解决了高能理论中著名的层次问题，其中规范场和希格斯场被统一在一个具有额外维度的高维规范理论框架中。在这个研究项目中，我们试图构建一个基于规范-希格斯统一场景的现实模型，它应该是标准模型之外的一些物理模型。更具体地说，我们提出了一个SU(3)规范模型(mod.Phys.Lett.A17(2002)2249)，作为实现这一情景的可能的最小模型。有趣的是，在规范-希格斯统一的情况下，规范群应该由普通的SU(2)Xu(1)扩展而来，从而不可避免地引出了一种“新物理”理论。我们进一步发展了这项研究，并讨论了几个剩余的重要问题。也就是说，我们发现通过引入规范群伴随表示的物质场等方法，解决了使用Hosotani机制时规范群的秩次不降低的问题。关于二维球的场论和转动对称性的自发破缺等。另一位研究者考虑了以二维球为外维，以单极组态为球中心背景场的场论。人们已经发现，在这些理论中，球体出现了一个临界半径，在那里，与球体相关的对称性，如旋转对称性，开始自发地破裂。

The main results obtained by this research project are listed below :1. Attempt to construct a realistic model based upon the Gauge-Higgs Unification scenario.The head investigator once proposed a scenario, in collaboration with Hatanaka and Inami, where the famous hierarchy problem of high energy theory is naturally solved by use of Gauge-Higgs Unification scheme, where gauge field and Higgs field are unified in a framework of higher dimensional gauge theory with extra dimension. In this research project, we attempted to construct a realistic model based upon the Gauge-Higgs Unification scenario, which should be some physics beyond the Standard Model. More concretely, we have proposed a SU(3) gauge model (Mod.Phys.Lett.A 17 (2002) 2249), as a possible minimal model to realize the scenario. It is interesting to note that in the Gauge-Higgs Unification scenario, gauge group should be extended from the ordinary SU(2)xU(1), thus inevitably leading a theory of "New Physics". We further developed the research, and discussed a few remaining important issues. Namely, we have found that the problem of no reduction of the rank of gauge group in the usage of Hosotani mechanism is solved by introducing matter fields belonging to the adjoint representation of the gauge group, etc.2. Field theories on the two dimensional sphere and the spontaneous breaking of rotational symmetry etc.Another investigator considered field theories with two dimensional sphere as its extra-dimension and with monopole configuration as a background field at the center of the sphere. It has been found that in these theories there appears a critical radius of the sphere, where symmetries associated with the sphere, such as rotational symmetry, start to break down spontaneously.