Brane world corrections to the scalar vacuum force in the Randall-Sundrum II-pscenario

Abstract

Vacuum force is an interesting low energy test for brane worlds due to its dependence on field's modes and its role in submillimeter gravity experiments. In this work, we generalize a previous model example: the scalar field vacuum force between two parallel plates lying in the brane of a Randall-Sundrum scenario extended by $p$ compact dimensions (RSII-$p$). Upon use of Green's function technique, for the massless scalar field, the 4D force is obtained from a zero mode while leading order corrections due to the noncompact dimension turn out attractive and depend on the separation between plates as ${l}^{\ensuremath{-}(6+p)}$. For the massive scalar field, a quasilocalized mode yields the 4D force with attractive corrections behaving like ${l}^{\ensuremath{-}(10+p)}$. Corrections are negligible with respect to 4D force for anti-de Sitter (${\mathrm{AdS}}_{(5+p)}$) radius much less than $\ensuremath{\sim}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{m}$. In the massless case we also determined, numerically, the corrections due to compact dimensions. To avoid conflict with experimental data we get $R\ensuremath{\le}0.4\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, $0.3\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ for the cases $p=1$, 2, respectively. Although the $p=0$ case is not physically viable due to the different behavior in regard to localization for the massless scalar and electromagnetic fields it yields a useful comparison between the dimensional regularization and Green's function techniques as we describe in the discussion.