Recovering the Negative Mode for Type B Coleman-de Luccia Instantons

TL;DR

This paper challenges the belief that type B Coleman-de Luccia instantons lack a negative mode, demonstrating that such a mode exists when considering a more general Euclidean path integral approach, and clarifies their thermal interpretation.

Contribution

It introduces the concept of a "purely geometric junction" to recover the negative mode for type B instantons, expanding understanding of their stability and interpretation.

Findings

Type B instantons possess a negative mode when the Euclidean path integral is less restricted.

The negative mode for type B instantons is explicitly constructed.

Type B and type A instantons share the same thermal tunneling interpretation.

Abstract

The usual (type A) thin-wall Coleman-de Luccia instanton is made by a bigger-than-half sphere of the false vacuum and a smaller-than-half sphere of the true vacuum. It has a the standard O(4) symmetric negative mode associated with changing the size of false vacuum region. On the other hand, the type B instanton, made by two smaller-than-half spheres, was believed to have lost this negative mode. We argue that such belief is misguided due to an over-restriction on Euclidean path integral. We introduce the idea of a "purely geometric junction" to visualize why such restriction could be removed, and then explicitly construct this negative mode. We also show that type B and type A instantons have the same thermal interpretation for mediating tunnelings.