Chiral Edge States in 2+1 Dimensional Topological Phases

TL;DR

This paper explores the representation of chiral edge states in 2+1D topological phases using constrained fermionic fields, highlighting their connection to chiral conformal field theories and addressing related gauge anomaly issues.

Contribution

It introduces a fermionic constrained fields framework for describing fractionalized edge states in topological phases, linked to chiral coset CFT structures.

Findings

Representation of edge states via constrained fermions

Connection to chiral coset conformal field theories

Handling of gauge anomalies in the fermionic description

Abstract

Chiral edge states of 2+1 dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and non-integer values of central charge, respectively. In this work we describe certain edge states in terms of constrained fermionic fields that realize chiral coset CFT structures. This construction arises naturally in the so-called quantum wires approach for topological phases and allows for representing fractionalized edge states directly in terms of fermionic degrees of freedom. At the same time, the constrained fermions description introduces some subtleties concerning gauge anomalies since it involves the coupling of chiral fermions to gauge fields. We describe in this article how to handle these issues.