Collective excitations at the boundary of a four-dimensional quantum Hall droplet

Abstract

In this work we investigate collective excitations at the boundary of a recently constructed four-dimensional (4D) quantum Hall state. Local bosonic operators for creating these collective excitations can be constructed explicitly. Massless relativistic wave equations with helicity S can be derived exactly for these operators from their Heisenberg equation of motion. For the $S=1$ and $S=2$ cases these equations reduce to the free Maxwell and linearized Einstein equations respectively. These collective excitations can be interpreted as hydrodynamical modes at the boundary of the 4D quantum Hall effect droplet. Outstanding issues are critically discussed.