Incompressible topological solitons

TL;DR

This paper introduces a new class of topological solitons called incompressible solitons, which cannot be confined to finite volumes due to their infinite energy, with examples in various dimensions including Skyrmions.

Contribution

The paper identifies and analyzes a novel class of topological solitons that are inherently incompressible and cannot be localized in finite volumes, expanding the understanding of soliton solutions.

Findings

Incompressible solitons exist in infinite volume spaces but have infinite energy in finite volumes.

Examples include (1+1)D kinks with nonstandard kinetic terms and Skyrmions in dielectric models.

In (3+1)D, Skyrmions can form a topological perfect fluid representing incompressible matter.

Abstract

We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy. These objects are, therefore, 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 vacummless) potentials. But incompressible solitons exist also in higher dimensions. As specific examples in (3+1) dimensions we study Skyrmions in the dielectric extensions both of the minimal and the BPS Skyrme models. In the the latter case, the skyrmionic matter describes a completely incompressible topological perfect fluid.