Note on Warped Compactification -- Finite Brane Potentials and Non-Hermiticity --

Abstract

We study radius stabilization in the Randall-Sundrum model without assuming any unnaturally large stabilizing scalar potential parameter at the boundary branes (${\hat{I}}^3$) by the frequently used superpotential method. Employing a perturbative expansion in $1/γ^2$ and the backreaction parameter, we obtain approximate analytical expressions for the radion mass and wavefunction. We validate them through a dedicated numerical analysis, which solves the linearized coupled scalar and metric field equations exactly. It is observed that the radion mass decreases with decreasing ${\hat{I}}^3$. Below a critical value of ${\hat{I}}^3$, the radion becomes tachyonic, suggesting destabilization of the extra dimension. We also address the issue of non-Hermiticity of the differential operator that determines the radion and Kaluza-Klein (KK) mode wavefunctions in the finite ${\hat{I}}^3$ limit. It is accomplished by finding an explicit form of the general scalar product that re-establishes the orthogonality in the KK decomposition.

23 pages, 2 figures, matches the published version