Anyons from Strings

TL;DR

The Nambu-Goto string in a three-dimensional (3D) Minkowski spacetime is quantized preserving Lorentz invariance and parity, and the spectrum of massive states contains anyons.

Abstract

The Nambu-Goto string in a 3-dimensional (3D) Minkowski spacetime is quantized preserving Lorentz invariance and parity. The spectrum of massive states contains anyons. An ambiguity in the ground state energy is resolved by the 3D N=1 Green-Schwarz superstring, which has massless ground states describing a dilaton and dilatino, and first-excited states of spin 1/4.