Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball

TL;DR

This paper investigates a flux-compactified model with an extended codimension-one brane, analyzing the landscape of de Sitter and Minkowski vacua, and demonstrating the stability of Minkowski solutions under symmetric perturbations.

Contribution

It introduces a stable, flux-compactified brane model free from delta-like brane issues, and characterizes the vacuum landscape with discrete flux and current parameters.

Findings

Minkowski vacua are isolated and occur at specific flux-current ratios.

De Sitter vacua form a discrete landscape labeled by integer flux and current.

Minkowski vacua are stable under axially-symmetric perturbations.

Abstract

We study a recently proposed model, where a codimension one brane is wrapped around the axis of symmetry of an internal two dimensional space compactified by a flux. This construction is free from the problems which plague delta-like, codimension two branes, where only tension can be present. In contrast, arbitrary fields can be localized on this extended brane, and their gravitational interaction is standard 4d gravity at large distance. In the first part of this note, we study the de Sitter (dS) vacua of the model. The landscape of these vacua is characterized by discrete points labeled by two integer numbers, related to the flux responsible for the compactification and to the current of a brane field. A Minkowski external space emerges only for a special ratio between these two integers, and it is therefore (topologically) isolated from the nearby dS solutions. In the second part, we show that the Minkowski vacua are stable under the most generic axially-symmetric perturbations (we argue that this is sufficient to ensure the overall stability).