Knots and Particles

TL;DR

This paper reports the discovery of stable knotted solitons in a 3+1 dimensional model using high performance computing, with potential implications for fundamental physics and observable phenomena in condensed matter systems.

Contribution

It demonstrates the existence of stable knotted solitons as finite energy solutions in a realistic 3+1D model, including explicit simulations of unknot and trefoil configurations.

Findings

Knotlike structures appear as stable solitons in the model

All torus knots are suggested to be realizable as solitons

Potential observability in nematic liquid crystals and superfluids

Abstract

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.