Analyzing the general conditions for modulus stabilization in a warped braneworld

Abstract

In braneworld scenarios with compact extra dimensions, the modulus field typically remains undetermined without an appropriate stabilization mechanism. A common approach introduces a bulk scalar field that generates an effective potential for the modulus with a stable minimum. In this work, we explore some novel aspects of such stabilization mechanisms. We study how the bulk scalar profile influences the stabilization procedure. Following the approach of Chacko et al. [1], we analyze several representative cases using methods of singular perturbation theory. We identify a consistent relationship between the structure of the bulk potential and the emergence of a stabilized modulus, and outline the general conditions that any bulk potential must satisfy to enable stabilization. In this context, we also examine a potential connection between geometric consistency conditions - specifically, the "brane world sum rules" - and the stabilized value of the modulus. In some scenarios where stabilization occurs, we find that these sum rules can offer additional constraints on the modulus, providing a complementary perspective on its determination. Taken together, these results offer a broader perspective on the mechanisms that govern modulus stabilization in higher-dimensional warped geometries.

Figures (7)

• Figure 1: Form of the bulk potential $V_b(\Phi)$ with $b=0.2$ for $\lambda = 1$ (left) and $\lambda=-1$ (right)
• Figure 2: Scalar field profile for parameter values $b=0.2, v=0.01, k=10, \alpha = 10^{-5}$ with $\lambda = 0.001$ (left) and $\lambda = -0.001$ (right)
• Figure 3: Effective radion potential (double well) for parameter values $b=0.2, v=0.01, k=10, \alpha = 10^{-5}$ with $\lambda = 0.001$ (left) and $\lambda = -0.001$ (right)
• Figure 4: BFG potentials for different p values
• Figure 5: Effective radion potential for p = 1 (top left), p = 3 (top right) and p = 5 (bottom)