Coherent State Induced Star-Product on $R^3_λ$ and the Fuzzy Sphere

Details Coherent State Induced Star-Product on $R^3_λ$ and the Fuzzy Sphere Coherent State Induced Star-Product on $R^3_λ$ and the Fuzzy Sphere

2001-10-31

arxiv.org/abs/hep-th/0110291v3

Phys.Rev.D66:025025,2002

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Latex file, no figures, v2: minor changes, typos corrected and some references added, v3: Final version to appear in

Scientific paper

10.1103/PhysRevD.66.025025

Using the Hopf fibration and starting from a four dimensional noncommutative Moyal plane, $R^2_{\theta}\times R^2_{\theta}$, we obtain a star-product for the noncommutative (fuzzy) $R^3_{\lambda}$ defined by $[x^i,x^j]=i\lambda\epsilon_{ijk}x^k$. Furthermore, we show that there is a projection function which allows us to reduce the functions on $R^3_{\lambda}$ to that of the fuzzy sphere, and hence we introduce a new star-product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on fuzzy sphere and $\rrlam$ from the corresponding field theories on $R_{theta}\times R_{\theta}$ space.

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