Chiral Modes of Giant Superfluid Vortices

We discuss rapidly rotating states of a superfluid. We concentrate on the Giant-Vortex (GV) state, which is a coherent rotating solution with a macroscopic hole at the center. We show that, for any trap, the fluctuations obey an approximately chiral dispersion relation, describing arbitrary shape deformations moving with the speed of the ambient superfluid. This dispersion relation is a consequence of a peculiar infinite symmetry group that emerges at large angular velocity and implies an infinite ground-state degeneracy. The degeneracy is lifted by small corrections which we determine both for smooth traps and the hard trap.