Embedding Fractional Quantum Hall Solitons in M-theory Compactifications

We engineer U(1)^n Chern-Simons type theories describing fractional quantum Hall solitons (QHS) in 1+2 dimensions from M-theory compactified on eight dimensional hyper-K\"{a}hler manifolds as target space of N=4 sigma model. Based on M-theory/Type IIA duality, the systems can be modeled by considering D6-branes wrapping intersecting Hirzebruch surfaces F_0's arranged as ADE Dynkin Diagrams and interacting with higher dimensional R-R gauge fields. In the case of finite Dynkin quivers, we recover well known values of the filling factor observed experimentally including Laughlin, Haldane and Jain series.