The Fuzzy S^4 by Quantum Deformation

Details The Fuzzy S^4 by Quantum Deformation The Fuzzy S^4 by Quantum Deformation

2002-12-18

arxiv.org/abs/hep-th/0212214v1

Nucl.Phys. B656 (2003) 325-343

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTex, no figure

Scientific paper

10.1016/S0550-3213(03)00104-4

The fuzzy algebra of S^4 is discussed by quantum deformation. To this end we embed the classical S^4 in the Kaehler coset space SO(5)/U(2). The harmonic functions of S^4 are constructed in terms of the complex coordinates of SO(5)/U(2). Being endowed with the symplectic structure they can be deformed by the Fedosov formalism. We show that they generate the fuzzy algebra \hat A_\infty (S^4) under the * product defined therein, by using the Darboux coordinate system. The fuzzy spheres of higher even dimensions can be discussed similarly. We give basic arguments for the generalization as well.

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