非最小耦合引力理论中的膜世界

After solving the gauge hierarchy problem by the curve of extra dimension, the famous Randall-Sundrum brane model has been applied extensively in many areas such as astronomy, cosmology and particle physics. A recent investigation found that the brane-world model based on the non-minimally coupling theories maybe give an alternative of solving the gauge hierarchy problem that will give different phenomenology from the Randall-Sundrum model. This project will study brane models in the non-minimally coupling theories and includes three parts: 1) We will construct new brane-world models under the frame of the non-minimally coupling gravities (include the scalar-tensor and vector-tensor gravities), then discuss stability of the brane solutions and localization of the graviton zero mode. We will also solve the gauge hierarchy problem by the new brane model. 2) We will investigate the localization problem of various bulk matter fields on the non-minimally coupling brane, and study the mass hierarchy problem between different generations of fermions in the Standard Model by the localization mechanism of fermions. 3) We will consider the interactions between various matter fields in the bulk, and discuss the corresponding new physical effects in the accelerators.

著名的Randall-Sundrum膜世界模型通过引入弯曲的额外维很好地解决了规范层次问题，并在天文学、宇宙学和粒子物理等学科领域得到了广泛的应用。最近的研究发现基于非最小耦合理论的膜世界模型则给出另一类解决规范层次问题的方案，其唯象学将不同于Randall-Sundrum模型。本项目将研究非最小耦合引力理论中的膜世界模型，研究内容分为三部分：1) 研究非最小耦合引力(包括标量-张量引力和矢量-张量引力)理论框架下新的膜世界解，探讨解的稳定性及引力零模的局域化，并解决规范层次问题；2) 研究非最小耦合膜世界上各种物质场的局域化问题，通过费米子局域化机制来研究标准模型中各代费米子之间的质量层次问题；3)研究高维时空中各种场之间的相互作用，探讨其在加速器中的新物理效应。

著名的Randall-Sundrum膜世界模型通过引入弯曲的额外维很好地解决了规范层次问题，并在天文学、宇宙学和粒子物理等学科领域得到了广泛的应用。该项目研究成果分为三部分：1) 由多标量场给出了膜阵列的解析解，发现费米子共振态简并的新现象；2) 给出五维渐进AdS时空中膜世界上U(1)规范场的局域化机制；3) 发现膜世界上矢量场的共振态模式可以作为暗物质的一种候选者。研究成果发表在JHEP、PRD和CQG等杂志上。这些研究成果加深了对额外维与膜世界的理解。