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 the standard $O(4)$ symmetric negative mode associated with changing the size of the true 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 a belief is misguided due to an overrestriction on the Euclidean path integral. We introduce the idea of a “purely geometric junction” to visualize why such a restriction could be removed, and then we explicitly construct this negative mode. We also show that type B and type A instantons have the same thermal interpretation for mediating tunnelings.

• Received 4 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.084026