The Physics of Large Extra Dimension

本研究项目取得的主要成果如下：1。尝试建立一个基于格-希格斯统一情景的现实模型。首席研究员曾与Hatanaka和Inami合作提出了一个方案，在该方案中，规范场和希格斯场统一在一个具有额外维度的高维规范理论框架中，通过使用规范-希格斯统一方案自然地解决了著名的高能理论层次问题。在这个研究项目中，我们试图建立一个基于格-希格斯统一情景的现实模型，这应该是标准模型之外的一些物理。更具体地说，我们提出了SU(3)规范模型（mod . phys.leet）。A 17(2002) 2249)，作为实现该场景的可能最小模型。有趣的是，在规范-希格斯统一情景中，规范群应该从普通的SU(2)xU(1)扩展，从而不可避免地导致“新物理”理论。我们进一步开展了研究，并讨论了几个剩下的重要问题。即通过引入属于规范群伴随表示的物质场等，我们发现了在使用细谷机制时规范群秩不降的问题。二维球的场论和旋转对称的自发破缺等。另一位研究者考虑了以二维球为其额外维，以单极子位形为球中心背景场的场论。人们发现，在这些理论中，出现了一个临界半径，在这个半径上，与球体相关的对称性，如旋转对称，开始自发地破坏。

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.