Charge and Magnetic Flux Correlations in Chern-Simons Theory with Fermions

TL;DR

This paper introduces charge and magnetic flux operators in Chern-Simons theory, showing their correlation functions are local, exactly evaluable, and reveal charge-flux condensation and anyonic states when coupled to fermions.

Contribution

It defines new operators in Chern-Simons theory, establishes their locality, and analyzes their correlation functions both exactly and via expansion, highlighting physical states with anyonic properties.

Findings

Magnetic flux creation operator is the Wilson line.

Correlation functions are local and exactly computed in pure case.

Charge and flux condensation leads to anyonic states.

Abstract

Charge and magnetic flux bearing operators are introduced in Chern-Simons theory both in its pure form and when it is coupled to fermions. The magnetic flux creation operator turns out to be the Wilson line. The euclidean correlation functions of these operators are shown to be local and are evaluated exactly in the pure case and through an expansion in the inverse fermion mass whenever these are present. Physical states only occur in the presence of fermions and consist of composite charge-magnetic flux carrying states which are in general anyonic. The large distance behavior of the correlation functions indicates the condensation of charge and magnetic flux.