On the relation between fractional charge and statistics

Abstract

We revisit an argument, originally given by Kivelson and Roček, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a $\nu =1/m$ Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a global one-form ${\mathcal{Z}}_m$ symmetry.

6 pages (single column), no figures. v2: Wrong normalization factor in Eq. (1) fixed. Added discussion about other filling fractions

References in corpus (6)

• Generalized Global Symmetries
• Condensate induced transitions between topologically ordered phases
• Quantum Hall Physics - hierarchies and CFT techniques
• Fractional charge and fractional statistics in the quantum Hall effects
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Anyons, 't Hooft loops and a Generalized Connection in Three Dimensions

Cited by in corpus (1)

• Anyonic analogue of optical Mach-Zehnder interferometer