Locally Localized Gravity Models in Higher Dimensions

TL;DR

This paper generalizes locally localized gravity models to higher dimensions, analyzing different brane types and demonstrating how gravitational interactions can confine bulk fields to the brane, with new relations involving brane cosmological constants.

Contribution

It introduces higher-dimensional extensions of localized gravity models, identifying conditions for field localization and the unique role of AdS branes in these models.

Findings

Higher-dimensional gravity models can be free of naked singularities.

Only AdS branes are physically meaningful in the higher-dimensional models.

Bulk gauge fields and massless fermions can be localized by gravity alone.

Abstract

We explore the possibility of generalizing the locally localized gravity model in five space-time dimensions to arbitrary higher dimensions. In a space-time with negative cosmological constant, there are essentially two kinds of higher-dimensional cousins which not only take an analytic form but also are free from the naked curvature singularity in a whole bulk space-time. One cousin is a trivial extension of five-dimensional model, while the other one is in essence in higher dimensions. One interesting observation is that in the latter model, only anti-de Sitter ($AdS_p$) brane is physically meaningful whereas de Sitter ($dS_p$) and Minkowski ($M_p$) branes are dismissed. Moreover, for $AdS_p$ brane in the latter model, we study the property of localization of various bulk fields on a single brane. In particular, it is shown that the presence of the brane cosmological constant enables bulk gauge field and massless fermions to confine to the brane only by a gravitational interaction. We find a novel relation between mass of brane gauge field and the brane cosmological constant.