New Scaling Limit for Fuzzy Spheres

Details New Scaling Limit for Fuzzy Spheres New Scaling Limit for Fuzzy Spheres

2002-09-16

arxiv.org/abs/hep-th/0209131v2

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, latex

Scientific paper

Using a new scaling limit as well as a new cut-off procedure, we show that $\phi^4$ theory on noncommutative ${\bf R}^4$ can be obtained from the corresponding theory on fuzzy ${\bf S}^2 \times {\bf S}^2$. The star-product on this noncommutative ${\bf R}^4$ is effectively local in the sense that the theory naturally has an ultra-violet cut-off $\Lambda$ which is inversely proportional to the noncommutativity $\theta$, i.e $ \Lambda= \frac{2}{\theta}$. We show that the UV-IR mixing in this case is absent to one loop in the $2-$point function and also comment on the $4-$point function.

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