4 research outputs found
Brane Realizations of Quantum Hall Solitons and Kac-Moody Lie Algebras
Using quiver gauge theories in (1+2)-dimensions, we give brane realizations
of a class of Quantum Hall Solitons (QHS) embedded in Type IIA superstring on
the ALE spaces with exotic singularities. These systems are obtained by
considering two sets of wrapped D4-branes on 2-spheres. The space-time on which
the QHS live is identified with the world-volume of D4-branes wrapped on a
collection of intersecting 2-spheres arranged as extended Dynkin diagrams of
Kac-Moody Lie algebras. The magnetic source is given by an extra orthogonal
D4-brane wrapping a generic 2-cycle in the ALE spaces. It is shown as well that
data on the representations of Kac-Moody Lie algebras fix the filling factor of
the QHS. In case of finite Dynkin diagrams, we recover results on QHS with
integer and fractional filling factors known in the literature. In case of
hyperbolic bilayer models, we obtain amongst others filling factors describing
holes in the graphene.Comment: Lqtex; 15 page
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.Comment: Latex, 14 pages. Modified version, to appear in IJGMM