Non-commutative geometry of 4-dimensional quantum Hall droplet

Details Non-commutative geometry of 4-dimensional quantum Hall droplet Non-commutative geometry of 4-dimensional quantum Hall droplet

2002-03-11

arxiv.org/abs/hep-th/0203095v2

Nucl.Phys.B638:220-242,2002

Physics

High Energy Physics

High Energy Physics - Theory

latex 22 pages, no figures. some references added. some results are clarified

Scientific paper

10.1016/S0550-3213(02)00499-6

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy $S^{4}$ appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in this non-commutative geometry, are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. It is discussed that some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory.

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