Hybrid compactifications and brane gravity in six dimensions

TL;DR

This paper investigates a six-dimensional warped braneworld model with two branes, demonstrating that four-dimensional Einstein gravity emerges at long distances despite extra scalar degrees of freedom, through linear perturbation analysis.

Contribution

It introduces a novel six-dimensional model with a conical 3-brane and a wrapped 4-brane, analyzing linear perturbations to show the emergence of effective 4D gravity.

Findings

Weak gravity is described by a scalar-tensor theory.

The extra scalar mode is suppressed at long distances.

Four-dimensional Einstein gravity is recovered on the brane.

Abstract

We consider a six-dimensional axisymmetric Einstein-Maxwell model of warped braneworlds. The bulk is bounded by two branes, one of which is a conical 3-brane and the other is a 4-brane wrapped around the axis of symmetry. The latter brane is assumed to be our universe. If the tension of the 3-brane is fine-tuned, it folds the internal two-dimensional space in a narrow cone, making sufficiently small the Kaluza-Klein circle of the 4-brane. An arbitrary energy-momentum tensor can be accommodated on this ring-like 4-brane. We study linear perturbations sourced by matter on the brane, and show that weak gravity is apparently described by a four-dimensional scalar-tensor theory. The extra scalar degree of freedom can be interpreted as the fluctuation of the internal space volume (or that of the circumference of the ring), the effect of which turns out to be suppressed at long distances. Consequently, four-dimensional Einstein gravity is reproduced on the brane. We point out that as in the Randall-Sundrum model, the brane bending mode is crucial for recovering the four-dimensional tensor structure in this setup.