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

TL;DR

This work studies the localization of KK modes of $q$-form fields on a five-dimensional RS-2 thick brane in squared curvature gravity by introducing a coupling function $F(R,\varphi)$ between the $q$-form fields, gravity, and a background scalar. The authors derive a KK decomposition in conformal coordinates, obtain Schrödinger-like equations with $V(z)$-type potentials, and extract normalizable zero modes along with the corresponding 4D effective actions. They analyze two coupling schemes, gravity coupling with $F(R,\varphi)=G(R)$ and background-scalar coupling with $F(R,\varphi)=\tilde{F}(\varphi)$, providing explicit forms for $G(R)$ and $\tilde{F}(\varphi)$, and show how the localization properties depend on parameters such as $C_2$ and $t$. The main results show that zero modes are localizable for all cases, while the spectra of massive modes and the required thresholds for localization depend sensitively on these parameters, with volcano-type potentials arising in several scenarios, offering potential phenomenological implications for higher-dimensional physics.

Abstract

Unlike the duality in four-dimensional spacetime, where the $q-$form fields corresponds to the scalar fields or the vector fields, in higher dimensional spacetime, they denote new types of particles. In this paper, we investigate the localization of the KK modes of the $q$-form fields in a five dimensional brane world. We introduce the coupling between the $q-$form fields and both the gravity and the background scalar field. This consideration enables the localization of the $q$-form fields on the five-dimensional RS-2 thick brane, leading to the derivation of zero modes, Schrödinger-like equations, and a four-dimensional effective action. We suggest a new function $F(R,\varphi)$ to stand for the coupling of the $q$-form field with gravity and background scalar fields. Our analysis highlights the significance of the parameters $\text C_2$ and $\displaystyle t$ in the localization processes.

Figures (9)

• Figure 1: The effective potentials $V_0\left(z\right)$ in (a), and the shapes of the scalar zero-mode $\chi_0\left(z\right)$ in (b). The parameters are set as $\text{C}_1=10,k=1$, and $\text{C}_2=0.3,0.5,0.7$.
• Figure 2: The upper row shows the potential $V_0\left(z\right)$ with the black line representing the potential and the colored lines indicating the position of mass spectra. The lower row presents the corresponding solutions of $\chi_n\left(z\right)$. Parameters are varied as $\text{C}_1=15,10,10; k=1$ and $\text{C}_2=0.5,0.5,0.6$, respectively.
• Figure 3: The effective potentials $V_\varphi(z)$ in (a), and the shapes of the scalar zero-mode $\chi_\varphi(z)$ in (b). The parameters are set as $\lambda=10, k=1$ and $t=1, 2, 3$.
• Figure 4: The effective potentials $V_1\left(z\right)$ in (a), and the shapes of the vector zero-mode $\rho_0\left(z\right)$ in (b). The parameters are set as $\text{C}_1=20, k=1$, and $\text{C}_2=0.4, 0.5, 0.6$.
• Figure 5: The upper row shows the potential $V_1\left(z\right)$ with the black line representing the potential and the colored lines indicating the position of mass spectra. The lower row presents the corresponding solutions of $\rho_n\left(z\right)$. Parameters are varied as $\text{C}_1=15,10,10; k=1$ and $\text{C}_2=0.5,0.5,0.6$, respectively.