Fractional Statistics and Chern-Simons Field Theory in 2+1 Dimensions

TL;DR

This paper explores how Chern-Simons field theories in 2+1 dimensions naturally give rise to anyons with fractional statistics, highlighting their theoretical properties and different realizations.

Contribution

It clarifies the role of the Chern-Simons term in enabling fractional statistics and discusses two approaches for realizing anyons in 2+1 dimensional field theories.

Findings

Fractional statistics is only possible in two spatial dimensions.

Chern-Simons term acts as a gauge field mass term.

Anyons can be solitons or fundamental quanta with fractional statistics.

Abstract

The question of anyons and fractional statistics in field theories in 2+1 dimensions with Chern-Simons (CS) term is discussed in some detail. Arguments are spelled out as to why fractional statistics is only possible in two space dimensions. This phenomenon is most naturally discussed within the framework of field theories with CS term, hence as a prelude to this discussion I first discuss the various properties of the CS term. In particular its role as a gauge field mass term is emphasized. In the presence of the CS term, anyons can appear in two different ways i.e. either as soliton of the corresponding field theory or as a fundamental quanta carrying fractional statistics and both approaches are elaborated in some detail.