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

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.

version 3, 18 pages, 6 figures, changed the title to follow the terminology of earlier works and expanded appendix to address the comments from Brown, Freivogel, Weinberg and Xiao

References in corpus (3)

• Thermal derivation of the Coleman-De Luccia tunneling prescription
• The number of negative modes of the oscillating bounces
• Horizons and Tunneling in the Euclidean False Vacuum