Abstract. Since the two pillars of modern physics: Quantum Field Theory and general relativity are incompatible, one tries to take fluctuating geometries into account through deforming space-time. The resulting noncommutative Quantum Field Theory shows the IR/UV mixing. We modify the action for a scalar model in 4 dimensions and show, that a renormalizable field theory results. For the proof we fist transform to a matrix model and use the Wilson- Polchinski approach to renormalization. An efficient power-counting theorem allows to eliminate all higher genus contributions. At a special point of the parameter space the model becomes self-dual, the beta function vanishes and the model connects to integrable systems.

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