Nucleation of vacuum phase transitions by topological defects

The Euclidean action is calculated in the thin-wall approximation for a first-order vacuum phase transition in which the bubble appears symmetrically around either a global monopole or a gauge cosmic string. The bubble is assumed to be much larger than the core size of the monopole or string. In both cases the value of the Euclidean action is shown to be reduced below the $O(4)$ symmetric action value, indicating that the topological defects act as effective nucleation sites for vacuum decay.