Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres

Details Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres

2003-10-30

arxiv.org/abs/hep-th/0310274v2

Phys.Lett. B602 (2004) 255-260

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 1 figure

Scientific paper

10.1016/j.physletb.2004.04.093

We construct higher dimensional quantum Hall systems based on fuzzy spheres. It is shown that fuzzy spheres are realized as spheres in colored monopole backgrounds. The space noncommutativity is related to higher spins which is originated from the internal structure of fuzzy spheres. In $2k$-dimensional quantum Hall systems, Laughlin-like wave function supports fractionally charged excitations, $q=m^{-{1/2}k(k+1)}$ (m is odd). Topological objects are ($2k-2$)-branes whose statistics are determined by the linking number related to the general Hopf map. Higher dimensional quantum Hall systems exhibit a dimensional hierarchy, where lower dimensional branes condense to make higher dimensional incompressible liquid.

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