A Brane model with two asymptotic regions

TL;DR

This paper constructs a six-dimensional brane model with two asymptotic regions, analyzing the scalar potential's role in the geometry and discussing the model's causal structure and gravity localization.

Contribution

It introduces a new cylindrically symmetric six-dimensional brane solution with dual asymptotic geometries and explores the impact of scalar potentials on the model's properties.

Findings

The model features two distinct asymptotic regions: Melvin-like and flat with conical singularity.

Gravity is not localized on the brane in this configuration.

The scalar potential's form influences the energy and geometric behavior of the solution.

Abstract

Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip.S.Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.