Continuous Structures

Abstract

AbstractWhen several distinct energy scales are involved, the vacuum symmetry is different for different length scales: the larger the length scale, the more the symmetry is reduced. The interplay of topologies on different length scales gives rise to many different types of topological objects, which are described by relative homotopy groups. This chapter discusses the continuous structures generated by relative homotopy groups, such as soliton terminating on a half-quantum vortex, skyrmion — the doubly quantized vortex in 3He-A, meron — the fraction of skyrmion, continuous structures in spinor Bose condensate and superconductors, semilocal strings in the Standard Model of particle physics, and the vortex sheet. The vortex sheet is the chain of alternating circular and hyperbolic merons concentrated inside the topological soliton in 3He-A and the chain of kinks in the domain wall in chiral superconductors. The chapter also discusses topological transitions between continuous textures, which are mediated by singular topological defects. For example, destruction of topological soliton in 3He-A occurs via creation of the loop of half-quantum vortex.