Three-dimensional generalization of anyon superconductivity

Abstract

A three-dimensional generalization of the wave function of Girvin et al. is constructed by taking the N\ensuremath{\rightarrow}\ensuremath{\infty} limit of a solution of the two-dimensional massless Dirac equation with an SU(N) gauge field. The resulting wave function is closely related to instanton solutions of the self-dual Einstein quations, and can be used to construct a multiparticle wave function with remarkable holonomy properties and a ground-state wave function with off-diagonal long-range order.