Stability of multibrane models

Multibrane 5-dimensional models with a warped extra spatial dimension compactified on an $S^1/Z_2$ orbifold are investigated. The Goldberger-Wise field, with appropriate bulk and brane potentials, is utilized to fix the brane positions. However, not all configurations with fixed brane positions are stable. Stability against small scalar perturbations of the metric and the Goldberger-Wise field was so far analyzed only for 2-brane models. Generalization of such analysis for multibrane models is the main subject of the present work. Stability of brane configurations is closely related to the spectrum of radions: namely, the existence of any tachyonic radion indicates instability, while models with positive squared masses for all radions are stable. The necessary and sufficient conditions for each of these possibilities are derived for multibrane models and constitute the main result of this paper. Additionally, some properties of radions, particularly their relation to distances between and along branes, are discussed.