Topologically protected vortex knots

As Lord Kelvin noted in a 1869 article, knotted vortex lines in an ideal fluid will remain forever knotted. However, the same is not true in non-idealized systems, as viscous flows may violate the conservation of knottedness. Here we investigate a version of vortex knot stability that holds for knots tied in the order parameter fields of certain condensed-matter systems. In our setting, the stability of a knot is a consequence of the nontrivial interaction between the knotting type of the vortex line and the topology of the corresponding order parameter space. We expect these results to be rather robust, as they are topological in nature, and therefore immune against local perturbations. We give concrete physical examples of this behavior, focusing mostly on spinor Bose--Einstein condensates.