(Meta)stable closed vortices in 3+1 dimensional gauge theories with an extended Higgs sector

TL;DR

This paper investigates stable, knotted vortex solutions in extended Higgs sector gauge theories, demonstrating their existence and stability in 3+1 dimensions and discussing their potential decay in higher dimensions.

Contribution

It introduces the concept of stable, closed vortices with knotted topology in gauge theories with extended Higgs sectors and provides numerical evidence for their existence.

Findings

Stable, knotted vortex solutions exist in certain gauge theories.

Numerical evidence supports the stability of toroidal vortex configurations.

Knotted vortices may decay in higher-dimensional spaces.

Abstract

In gauge theories with an extended Higgs sector the classical equations of motion can have solutions that describe stable, closed finite energy vortices. Such vortices separate two disjoint Higgs vacua, with one of the vacua embedded in the other in a manner that forms a topologically nontrivial knot. The knottedness stabilizes the vortex against shrinkage in 3+1 dimensional space-time. But in a world with extra large dimensions we expect the configuration to decay by unknotting. As an example we consider the semilocal $\theta_W \to \frac{\pi}{2}$ limit of the Weinberg-Salam model. We present numerical evidence for the existence of a stable closed vortex, twisted into a toroidal configuration around a circular Higgs vacuum at its core.