Solitonic Island in the Bubble

We review how the continuous symmetry can support a soliton inside a hightemperature bubble at the time of its nucleation. This solitonic island in disoriented phase remains stable during the growth of bubbles before their collision. There exists a well-established semiclassical theory of the first-order phase transition of which the process is described by the formation and the growth of bubbles [1, 2]. The scenario claimed by this theory is summarized as follows: In order to understand the basic features of first-order phase transition, it is sufficient to consider a model of a real scalar field of which the scalar potential has a false vacuum and a true vacuum. Then there is unique decay channel described by a well-known (Euclidean) bounce solution and the inside of the bubble does not contain any matter lump at the moment of its nucleation. Though the above results have been obtained in a specific series of models of a real scalar field [2, 3], it is widely believed that, when the bubble is nucleated, such results may not be changed much for more general cases, e.g. the inclusion of continuous symmetries or gauge fields [4], but not the gravitational field [5]. When we consider the first-order phase transition by thermal fluctuation, the similar formalism based on the O(3)-symmetric bubble solution can also be applied [3]. Here several questions may be arisen in accord with the principles of gauge theories: 1. Why does the continuous symmetry play no important role at the time of bubble nucleation?