标题： $q$-形式场在平方曲率引力域壁膜上与引力和背景标量的耦合 localization 显示英文标题

标题： Localization of $q$-form field on squared curvature gravity domain wall brane coupling with gravity and background scalar

摘要： 在本文中，我们研究了一个$q$-形式场，表示为$\displaystyle X_{M_1M_2...M_q}$，其中$\displaystyle q$表示指标的数量，特殊情况下$\displaystyle q = 0, 1, 2$分别对应标量场、矢量场和Kalb-Ramond场。 与四维时空中标量场和矢量场之间的对偶性不同， $q$-形式场在高维空间中对应更广泛的粒子。 我们提出了一种新颖的局部化Kaluza-Klein分解方法，用于五维时空中的$q$-形式场，考虑其与引力和背景标量场的耦合。 这种方法成功地将$q$-形式场局域化在域壁膜上，从而推导出零模、薛定谔型方程和四维有效作用量。 此外，为了表示$q$形式场与背景时空的引力和标量场的耦合，我们提出一个新的耦合函数$F(R,\varphi)$。 我们的分析突出了参数$\displaystyle C_2$和$\displaystyle t$在定位过程中的重要性。 显示英文摘要

摘要： In this paper, we investigate a $q$-form field, represented as $\displaystyle X_{M_1M_2...M_q}$, where $\displaystyle q$ indicates the number of indices, with special cases $\displaystyle q = 0, 1, 2$ corresponding to the scalar fields, vector fields, and Kalb-Ramond fields, respectively. Unlike the duality observed between scalar and vector fields in four-dimensional spacetime, $q$-form fields in higher dimensions correspond to a wider array of particles. We propose a novel localized Kaluza-Klein decomposition approach for the $q$-form field in a five-dimensional spacetime, considering its coupling with gravity and background scalar fields. This methodology enables the successful localization of the $q$-form field on a domain wall brane, leading to the derivation of zero modes, Schr\"{o}dinger-like equations, and a four-dimensional effective action. Additionally, in order to stand for the coupling of the $q$-form field with gravity and scalar fields of the background spacetime, we propose a new coupling function $F(R,\varphi)$. Our analysis highlights the significance of the parameters $\displaystyle C_2$ and $\displaystyle t$ in the localization process.