Speaker
Description
The Higgs mechanism in gauge theories can give rise to topological solitons. Nontrivial homotopy groups of the vacuum manifold can support different types of topological solitons. In this talk, we focus on vortices associated with the first homotopy group. Unlike higher homotopy groups, the first homotopy group can be non-Abelian. This non-Abelian structure may give rise to vortex phenomena that are qualitatively different from those of Abelian vortices. We consider a (3+1)-dimensional SO(3) gauge theory Higgsed to the tetrahedral group A_4. The fundamental group of the vacuum manifold SO(3)/A_4 is the binary tetrahedral group, providing a concrete realization of non-Abelian vortices. We construct finite-tension vortex solutions associated with order-two and order-three elements of A_4 and analyze their linear stability against fluctuations of the gauge and Higgs fields. We find that the non-Abelian structure gives rise to qualitatively different stability properties for these two types of vortices.