Brane world corrections to scalar vacuum force in RSII-p

TL;DR

This paper investigates how brane world models, specifically the RSII-$p$ scenario, modify the scalar vacuum force between parallel plates, revealing attractive corrections that depend on the number of extra dimensions and the scalar field's mass.

Contribution

It extends previous models by analyzing scalar vacuum forces in RSII-$p$ scenarios with compact dimensions, providing explicit correction formulas and comparing computational techniques.

Findings

Corrections depend on separation as $l^{-(6+p)}$ for massless scalars.

Massive scalars exhibit corrections scaling as $l^{-(10+p)}$.

Corrections are negligible for AdS radius less than $ extasciitilde 10^{-6}$m.

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 corrections turn out attractive and depend on the separation between plates as $l^{-(6+p)}$. For the massive scalar field a quasilocalized mode yields the 4D force with attractive corrections behaving like $l^{-(10+p)}$. Corrections are negligible w.r.t. 4D force for $AdS_{(5+p)}$ radius less than $\sim 10^{-6}$m. 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 an useful comparison between the dimensional regularization and Green's function techniques as we describe in the discussion.