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

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.