Incompressible topological solitons

Abstract

We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., Rn, but they cannot be placed in any finite volume because the resulting formal solutions have infinite energy. Therefore, these objects are interpreted as totally incompressible solitons. As a first particular example, we consider (1+1)-dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacuumless) potentials. But incompressible solitons also exist in higher dimensions. As specific examples, in (3+1) dimensions we study Skyrmions in the dielectric extensions of both the minimal and BPS Skyrme models. In the latter case, the Skyrmionic matter describes a completely incompressible topological perfect fluid