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.
Highlights
Topological solitons are ubiquitous objects in modern physics, both from a theoretical point of view and in a variety of applications [1,2]
We discover a new class of topological solitons
All known solitons have nonzero compressibility and can be squeezed to smaller sizes with a finite amount of energy. It is the aim of the current paper to prove the existence of a new class of topological solitons which, they exist in an infinite-volume space, e.g., in M 1⁄4 Rn, cannot be squeezed to a finite volume, which means that their compressibility is zero
Summary
Topological solitons are ubiquitous objects in modern physics, both from a theoretical point of view and in a variety of applications [1,2]. It is the aim of the current paper to prove the existence of a new class of topological solitons which, they exist in an infinite-volume space, e.g., in M 1⁄4 Rn, cannot be squeezed to a finite volume, which means that their compressibility is zero This possibility can be understood from the independence of the two topological bounds. As we will show below, it may happen that for a given solitonic model the constant C is finite while CvolðMÞ 1⁄4 ∞, which prevents the existence of finite-energy solutions with nontrivial values of the topological charge in a finite space In a sense, this new class is exactly opposite to compactons, which even without pressure are finitevolume objects.
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