On Fractional Quantum Hall Solitons and Chern-Simons Quiver Gauge Theories

TL;DR

This paper explores the theoretical modeling of fractional quantum Hall systems using Chern-Simons quiver gauge theories derived from M-theory and type IIA string theory, providing new insights into their geometric and flux configurations.

Contribution

It introduces a novel framework connecting fractional quantum Hall solitons with Chern-Simons quiver gauge theories from M-theory and type IIA string theory, including explicit flux and geometric calculations.

Findings

Derived filling factors for specific geometries like CP^2 and Hirzebruch surfaces.

Established a duality-based approach linking M-theory, type IIA, and FQHS systems.

Provided a geometric interpretation of magnetic sources in FQHS models.

Abstract

We investigate a class of hierarchical multiple layers of fractional quantum Hall soliton (FQHS) systems from Chern-Simons quivers embedded in M-theory on the cotangent on a 2-dimensional complex toric variety \bf V^2, which is dual to type IIA superstring on a 3-dimensional complex manifold \bf {CP}^1\times V^2 fibered over a real line \mathbb{R}. Based on M-theory/Type IIA duality, FQHS systems can be derived from wrapped D4-branes on 2-cycles in \bf {CP}^1\times V^2 type IIA geometry. In this realization, the magnetic source can be identified with gauge fields obtained from the decomposition of the R-R 3-form on a generic combination of 2-cycles. Using type IIA D-brane flux data, we compute the filling factors for models relying on \bf{CP}^2 and the zeroth Hirzebruch surface.