Fractional Quantum Hall Filling Factors from String Theory using Toric Geometry

Abstract

Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding Chern-Simons type models from M-theory compactified on four complex dimensional hyper-Kähler manifolds X^4. These manifolds, which are viewed as target spaces of a particular N=4 sigma model in two dimensions, are identified with the cotangent bundles over intersecting 2-dimensional toric varieties V_i^2 according to toric Cartan matrices. Exploring results of string dualities, the presented FQHE can be obtained from D6-banes wrapping on such intersecting toric varieties interacting with R-R gauge fields. This string theory realization provides a geometric interpretation of the filling factors in terms of toric and Euler characteristic topological data of the compactified geometry. Concretely, explicit bilayer models are worked out in some details.

17 pages, latex

References in corpus (7)

• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Theoretical expectations for a fractional quantum Hall effect in graphene
• Qubits from Adinkra Graph Theory via Colored Toric Geometry
• Determining the filling factors of fractional quantum Hall states using knot theory