Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory

TL;DR

This paper explores the connection between braid and exclusion statistics in one-dimensional systems using Chern-Simons theory, highlighting conditions under which these statistics are related or independent, and discusses bosonization of anyonic systems.

Contribution

It provides a theoretical analysis of the relationship between braid and exclusion statistics in 1D, including the role of anomalies and a discussion on bosonization via T-duality.

Findings

Anomalous matter actions establish a clear relation between braid and exclusion statistics.

Non-anomalous systems may have unconnected braid and exclusion statistics.

Bosonization of 1D anyonic systems can be achieved through T-duality.

Abstract

The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.