### Abstract

We study the quantization of a noncommutative \phi^3 model on the 4-dimensional quantum plane, by mapping it to the Kontsevich model. The model is shown to be renormalizable, using known results for the Kontsevich model, in particular its relation to integrable systems. This allows to obtain the genus expansion of the free energy and of any n-point function, which are finite for each genus after renormalization. A critical coupling is determined, beyond which the model is unstable. This provides a nontrivial interacting NC field theory in 4 dimensions. The case of 2 and 6 dimensions will also be discussed.

### Related Links

- http://lanl.arxiv.org/abs/hep-th/0603052 - paper on the arXive
- http://lanl.arxiv.org/abs/hep-th/0512203 - also relevant (previous) paper