膜世界理论，不仅为解决理论物理中的层次问题及宇宙学常数问题提供了新途径，并且在粒子物理及宇宙学中得到了广泛的应用和推广。该理论中一个重要的问题是研究各种物质场的KK模式，从而为额外维的存在性提供理论或实验依据。本项目将研究弯曲p-膜世界中任意的q-形式场及其对偶场的KK模式，主要包括三方面的内容： 1)首先，用解析或数值方法求解弯曲p-膜的薄膜和厚膜解，包括anti-de Sitter及de Sitter膜的求解，并分析其性质；2)其次，利用KK分解及KK约化的方法，研究q-形式场在膜上的局域化机制，并结合所得到的p-膜世界解，求解q-形式场KK模式的质量谱，分析膜上的有效宇宙学常数等参数对质量谱的影响；3)同时，寻找q-形式场的对偶场在p-膜世界上的局域化机制，得到膜上的Hodge对偶关系，比较分析q-形式场及其对偶场KK模式质量谱的异同，寻找额外维存在的新物理效应及相关的实验迹象。

The brane-world theory, which opens the new way to solve the hierarchy problem and the cosmological constant problem, has been widely applied and generalized on the particle physics and cosmology physics. One of the most important work in the theory is to investigate the KK modes of various matter fields, in order to offer some theoretical or experimental support for the existence of the extra dimensions. In this project, we will investigate the KK modes of the q-form field and its dual field on warped p-branes, which contains three parts: 1)Firstly, we will find the solutions of the thin and thick warped p-branes using analytic or numerical method, including the anti-de Sitter and de Sitter cases, and analyze their character. 2) Secondly, by the KK decomposition and the KK reduction method, we try to seek for a localization mechanism for the q-form field on the brane, with which we can work out the mass spectrum of their KK modes on the p-branes, and discuss the effect of the effective cosmological constant and other parameters on the mass spectrum. 3) Lastly, we will investigate how to localize the dual field of the q-form field, obtain the Hodge duality on the brane, compare the difference between the mass spectrum of the q-form field and its dual field, and finally find some new physical effect and experimental evidence of the extra dimensions.