On fractional quantum Hall solitons and Chern-Simons quiver gauge theories

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 two-dimensional complex toric variety V-2, which is dual to type IIA superstring on a three-dimensional complex manifold CP1 x V-2 fibered over a real line R. Based on M-theory/type IIA duality, FQHS systems can be derived from wrapped D4-branes on 2-cycles in CP1 x 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 CP2 and the zeroth Hirzebruch surface.