Brane modeling in warped extra-dimension

TL;DR

This paper explores five-dimensional warped brane models with scalar fields, discussing periodic and non-compact extra dimensions, and addresses the hierarchy problem while analyzing stability under perturbations.

Contribution

It introduces a scalar field configuration for branes, derives a generalized sum rule, and constructs a stable warped geometry model with two branes addressing the hierarchy problem.

Findings

Derived a generalized Gibbons-Kallosh-Linde sum rule.

Constructed a stable two-brane warped model.

Showed how Higgs localization solves the hierarchy problem.

Abstract

Five-dimensional scenarios with infinitesimally thin branes replaced by appropriate configurations of a scalar field were considered. A possibility of periodic extra dimension was discussed in the presence on non-minimal scalar-gravity coupling and a generalized Gibbons-Kallosh-Linde sum rule was found. In order to avoid constraints imposed by periodicity, a non-compact spacial extra dimension was introduced. A five dimensional model with warped geometry and two thin branes mimicked by a scalar profile was constructed and discussed. In the thin brane limit the model corresponds to a set-up with two positive-tension branes. The presence of two branes allows to address the issue of the hierarchy problem which could be solved by the standard warping of the four dimensional metric provided the Higgs field is properly localized. Stability of the background solution was discussed and verified in the presence of the most general perturbations of the metric and the scalar field.