NC Effective Gauge Model for Multilayer FQH States

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.

A matrix model for bilayered quantum Hall systems

“…which is nothing but the confining potential (20). This means that the kinetic energy is negligible compared to V .…”

D-string fluid in conifold: II. Matrix model for D-droplets on and

“…5) 6) and implying that the wave functions describing droplets on the 2-sphere should depend on three quantum numbers as shown below,…”

On Mass Gap in Type Iib Quantum Hall Solitons

“…Quantum Hall effect is one of the most interesting strongly correlated electron system in condensed matter physics [1]. At low energies, this effect which is described by a topological field theory has been subject to great interest not only because of its experimental results but also from its connection with recent developments in string theory [2,3,4,5].…”