Brane Localization and Stabilization via Regional Physics

TL;DR

This paper investigates how local and global effects in extra-dimensional models can naturally stabilize the position of a brane, using toy models like hyperbolic horns and cones to illustrate the mechanisms involved.

Contribution

It introduces a regional physics approach to brane stabilization, combining local and global effects in non-trivial extra-dimensional geometries.

Findings

Stable brane positions can be achieved through competing energy effects.

Both local and global geometrical effects contribute to stabilization.

Stability can occur even with broken symmetries in the extra dimensions.

Abstract

Extra-dimensional scenarios have become widespread among particle and gravitational theories of physics to address several outstanding problems, including cosmic acceleration, the weak hierarchy problem, and the quantization of gravity. In general, the topology and geometry of the full spacetime manifold will be non-trivial, even if our ordinary dimensions have the topology of their covering space. Most compact manifolds are inhomogeneous, even if they admit a homogeneous geometry, and it will be physically relevant where in the extra-dimensions one is located. In this letter, we explore the use of both local and global effects in a braneworld scenario to naturally provide position-dependent forces that determine and stabilize the location of a single brane. For illustrative purposes, we consider the 2-dimensional hyperbolic horn and the Euclidean cone as toy models of the extra-dimensional manifold, and add a brane wrapped around one of the two spatial dimensions. We calculate the total energy due to brane tension and bending (extrinsic curvature) as well as that due to the Casimir energy of a bulk scalar satisfying a Dirchlet boundary condition on the brane. From the competition of at least two of these effects there can exist a stable minimum of the effective potential for the brane location. However, on more generic spaces (on which more symmetries are broken) any one of these effects may be sufficient to stabilize the brane. We discuss this as an example of physics that is neither local nor global, but regional.