Bubble with Global Monopole

The first-order phase transition of O(3) symmetric models is considered in the limit of high temperature. It is shown that this model supports a new bubble solution where the global monopole is formed at the center of the bubble in addition to the ordinary O(3) bubble. Though the free energy of it is larger than that of normal bubble, the production rate can considerably be large at high temperatures. Since a general theory of the decay of the metastable phase was developed [1, 2], the study of first-order phase transitions have attracted the attention due to their possible relevance to the physics of the early universe. The semiclassical expression of the tunneling rate from false vacuum to true vacuum is given by the bubble solution of lowest (Euclidean) action both for the first-order phase transitions at zero temperature field theories [2] and those at finite temperature [3, 4]. However, the above case does not include the possibility that there exist various decay modes between two given classical vacua. In this note, we explore such problem by examining a scalar model of internal O(3) symmetry at finite temperature and examine a new bubble solution with a global monopole. Suppose that the model of our interest contains a series of stationary points which support bubble solutions, a decay probability per unit time per unit volume is given by