NC Effective Gauge Model for Multilayer FQH States

TL;DR

This paper introduces a noncommutative effective field theory for complex fractional quantum Hall states, including multilayer and hierarchical systems, using D-brane and fiber bundle techniques to classify and model these states.

Contribution

It develops a novel noncommutative field model for non-Laughlin FQH states, extending Susskind's theory to multilayer and hierarchical systems with explicit fiber bundle constructions.

Findings

Classifies FQH states via D-brane and fiber bundle methods.

Derives general NC and commutative models for FQH states.

Provides explicit expressions for rational filling factors and gauge symmetries.

Abstract

We develop an effective field model for describing FQH states with rational filling factors that are not of Laughlin type. These kinds of systems, which concern single layer hierarchical states and multilayer ones, were observed experimentally; but have not yet a satisfactory non commutative effective field description like in the case of Susskind model. Using $D$ brane analysis and fiber bundle techniques, we first classify such states in terms of representations characterized, amongst others, by the filling factor of the layers; but also by proper subgroups of the underlying $U(n) $ gauge symmetry. Multilayer states in the lowest Landau level are interpreted in terms of systems of $D2$ branes; but hierarchical ones are realized as Fiber bundles on $D2$ which we construct explicitly. In this picture, Jain and Haldane series are recovered as special cases and have a remarkable interpretation in terms of Fiber bundles with specific intersection matrices. We also derive the general NC commutative effective field and matrix models for FQH states, extending Susskind theory, and give the general expression of the rational filling factors as well as their non abelian gauge symmetries.