Thin limit of the 6D Cascading DGP model

TL;DR

This paper develops a non-perturbative, covariant thin limit formulation of the 6D Cascading DGP model by systematically reducing from thick branes to thin branes, deriving junction conditions and analyzing the class of thin sources.

Contribution

It introduces a two-step thin limit procedure for the 6D Cascading DGP model, deriving covariant junction conditions for the codimension-2 brane.

Findings

Derived covariant junction conditions for the thin codimension-2 brane.

Established a systematic two-step thin limit process.

Analyzed the class of thin source configurations compatible with the model.

Abstract

A thin limit description of the 6D Cascading DGP model is derived, starting from a configuration where both the codimension-1 and the codimension-2 branes are thick. Postulating that the thicknesses of the two branes obey a hierarchic relation, the thin limit is executed in two steps. First the thin limit of the codimension-1 brane is executed, obtaining a system where a "ribbon" codimension-2 brane is embedded inside a thin codimension-1 brane with induced gravity, and then the thin limit of the ribbon brane is considered. By proposing a geometric ansatz on the limit configuration, the junction conditions which are to hold at the thin codimension-2 brane are derived. The latters are fully non-perturbative and covariant and, together with the Israel junction conditions at the codimension-1 brane and the Einstein equations in the bulk, constitute the looked-for thin limit formulation of the 6D Cascading DGP model. It is commented on how wide is the class of thin source configurations which can be placed on the thin codimension-2 brane.