Thin-wall vacuum decay in the presence of a compact dimension

TL;DR

This paper extends the analysis of false vacuum decay to higher dimensions with gravity, providing explicit formulas for decay processes involving a compact dimension, generalizing Coleman and de Luccia's work.

Contribution

It introduces explicit formulas for vacuum decay in the presence of a compact dimension within the thin-wall approximation, broadening the theoretical understanding of such transitions.

Findings

Derived explicit Euclidean Bounce configurations for compact dimensions.

Generalized vacuum decay transition probabilities to higher dimensions.

Extended Coleman-de Luccia results to include compactified spaces.

Abstract

We study the problem of false vacuum decay in arbitrary dimensions, in the presence of gravity, and compute the transition probability within the thin-wall approximation, generalising the results of Coleman and de Luccia. In the particular case of one compact dimension, we present explicit formulae for the Euclidean Bounce configuration that drives the transition from a de Sitter to Minkowski or from a Minkowski to anti-de Sitter vacua.