Non-Abelian fractional quantum Hall states and chiral coset conformal field theories

TL;DR

This paper develops an effective Lagrangian framework using non-Abelian Chern-Simons actions to describe the low-energy bulk properties of non-Abelian fractional quantum Hall states, linking topological field theory with conformal field theories.

Contribution

It introduces a novel effective Lagrangian approach that captures a broad class of non-Abelian fractional quantum Hall states through topological Chern-Simons and chiral conformal field theories.

Findings

Provides a unified description of non-Abelian FQH states

Establishes a connection between Chern-Simons theory and conformal field theories

Enables analysis of topological properties of FQH states

Abstract

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern-Simons (CS) actions. Our approach exploits the connection between the topological Chern-Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.