The Thin-Wall Approximation in Vacuum Decay: a Lemma

TL;DR

This paper clarifies the thin-wall approximation in vacuum decay, proving it provides bounds on the decay rate and offering a simple criterion for vacuum instability with gravity.

Contribution

It demonstrates that two distinct thin-wall approximations bracket the true decay rate and generalizes the lemma to include gravitational effects.

Findings

Two thin-wall approximations serve as upper and lower bounds.

In the thin-wall limit, the bounds converge.

A generalized lemma offers a criterion for vacuum instability with gravity.

Abstract

The 'thin-wall approximation' gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for non-perturbative vacuum instability.