Superfluid vortices in four spatial dimensions

Quantum vortices in superfluids have been an important research area for many decades. Naturally, on this topic has focused two and three-dimensional superfluids, which vortex cores form points lines, respectively. Very recently, however, there growing interest the quantum simulation of systems with four spatial dimensions; raises question how would behave a higher-dimensional superfluid. In paper, we begin to establish phenomenology 4D under rotation, where core can plane. 4D, most generic type rotation is "double rotation" angles (or frequencies). We show, by solving Gross-Pitaesvkii equation, that simplest case equal-frequency double stabilise pair planes intersecting at point. This opens up wide number future topics, including unequal-frequency rotations; stability reconnection dynamics surfaces; possibility closed surfaces.