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第 37 卷 第 2 期, pp.41-79  (2017) [ 39页 ]

额外维与厚膜模型简介

刘玉孝
1 兰州大学物理科学与技术学院理论物理研究所,兰州730000

钟渊
2 西安交通大学理学院,西安710049

杨科
3 西南大学物理科学与技术学院,重庆400715

2017/06/07 发布

额外维概念的提出已有近百年的历史,但直到最近二十余年,人们对额外维物理的认识才发生了实质性的转变。例如,人们开始注意到额外维的尺度可以达到TeV-1 量级甚至是无穷大的,而不与当前的实验观测相违背。一些额外维模型还可以对粒子物理学中的规范层次问题以及宇宙学中的暗物质问题给出全新的解释。此外,如果将我们所处的四维世界看成是更高维时空中的拓扑缺陷,例如五维时空中的一个四维畴壁,则可以通过场论的方法得到局域在畴壁上的各种四维物质场。如果进一步要使四维牛顿引力也能被局域在畴壁上,一般需要假设五维时空按照某种方式弯曲。这种弯曲时空中的畴壁称为厚膜。最简单的解析厚膜解可以在广义相对论中通过引入最小耦合的背景标量场得到。随着宇宙学的发展,越来越多的扩展引力理论和非最小耦合的标量场相继被提出并被应用于宇宙学和高能物理的各种问题中。因此研究各种扩展引力和非最小耦合标量场理论中的解析厚膜解和各种场的局域化机制就成了一个重要而又有趣的方向。目前国内外对厚膜模型的研究已经取得了一系列的研究成果,我们将对这一领域的相关研究进行简单的介绍。本文先对几种常见的额外维模型包括Kaluza-Klein 理论、大额外维模型、Randall-Sundrum 模型和标准的厚膜模型进行简单介绍,并分析线性涨落和引力场的局域化。然后介绍厚膜背景下各种物质场的局域化机制。最后以非正则标量场论和几种常见的扩展引 力理论为例,介绍厚膜模型的相关研究进展。
The concept of extra dimensions has been proposed for about one hundred years,but only until the last twenty years or so, our knowledge on extra dimensions began to change essentially. For instance, people start to notice that the size of extra dimensions can be as large as TeV-1 scale or even infinitely large, without conflicting with nowadays experimental data. Some models on extra dimensions can offer completely new explanations to the hierarchy problem in particle physics and to the dark matter problem in cosmology. Besides, by regarding our four-dimensional world as a topological defect in higher-dimensional spaces, for example a fourdimensional domain wall in five-dimensional space-time, one would obtain various kinds of fourdimensional matter fields localized on the domain wall by using field theory methods. In order to localize the four-dimensional gravity on the wall, one usually needs to assume that the spacetime is curved in particular way. Such domain walls in curved space-time are called thick branes. The simplest analytic thick brane solution can be obtained in general relativity by introducing a minimally coupled background scalar field. With the development of cosmology, more and more extended gravity theories and non-minimally coupled scalar fields have been proposed and applied in many issues in high energy physics as well as in cosmology. Therefore, it is an interesting direction to study analytic thick brane solutions and the localization mechanism for different fields in various kinds of extended gravity theories and in non-minimally coupled scalar field theories. Nowadays, thick brane models have been extensively investigated both in China and abroad, and many results have been obtained. We are going to give a short introduction to the related results in this field. Firstly, we briefly introduce several typical models on extra dimensions, including the Kaluza-Klein theory, the large extra dimension model, the Randall-Sundrum model and the standard thick brane model, and analyze the linear perturbation as well as the localization of gravitational field. Then we discuss the localization mechanism of various matter fields in thick brane background. Finally, by using the non-canonical scalar field and several popular extensive gravitational theories, we introduce the development on the study of thick brane models.

全文: [PDF]
中图分类号: O412
关键词: 额外维;膜世界;引力理论;局域化;质量谱
Extra dimesions; Braneworld; Gravitational theory; Localization; Mass spectrum