Fractional spin from gravity

Abstract

Friedman and Sorkin have observed that the total angular momentum of an asymptotically flat, vacuum, quantum gravitational field in 3+1 dimensions need not be integral. We pursue this idea in the context of asymptotically flat 2+1 gravity, which is an exactly solvable model. We find that, for nontrivial spatial topologies, the quantized pure gravitational field has states of fractional spin. These states are dynamically allowed, in the sense that they solve all the constraints of the theory.