Static solutions in the R^4 brane world

TL;DR

This paper explores static solutions in a five-dimensional brane world model with higher curvature corrections, revealing that the radion is no longer a zero mode and highlighting the need for fine-tuning brane tensions to address the hierarchy problem.

Contribution

It introduces a novel brane world model with a $(Ricci-scalar)^4$ correction, providing numerical solutions and analyzing the implications for brane tensions and the radion mode.

Findings

Radion is not a zero mode in this model.

Negative brane tension is required for solutions.

Fine-tuning of brane tensions is necessary for hierarchy.

Abstract

A simple five-dimensional brane world model is proposed, motivated by M-theory compactified on a six-dimensional manifold of small radius and an $S^1/Z_2$ of large radius. We include a leading-order higher curvature correction to the tree-level bulk action since in brane world scenarios the curvature scale in the bulk may be comparable to the five-dimensional Planck scale and, thus, higher curvature corrections may become important. As a tractable model of the bulk theory we consider pure gravity including a $(Ricci-scalar)^4$-correction to the Einstein-Hilbert action. In this model theory, after a conformal transformation to the Einstein frame, we numerically obtain static solutions, each of which consists of a positive tension brane and a negative tension brane. For these solutions, we obtain two relations between the warp factor and the brane tensions. The existence of these relations implies that, contrary to the original Randall-Sundrum model, the so called radion is no longer a zero mode. We conclude that the tension of our brane should be negative and that fine-tuning of the tension of both branes is necessary for a large warp factor to explain the large hierarchy between the Planck scale and the electroweak scale.