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.

arXiv comment17 pages, latex

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