Exact renormalization of a noncommutative \phi^3 model in 6 dimensions

The noncommutative selfdual \phi^3 model in 6 dimensions is quantized and essentially solved, by mapping it to the Kontsevich model. The model is shown to be renormalizable and asymptotically free, and solvable genus by genus. It requires both wavefunction and coupling constant renormalization. The exact (all-order) renormalization of the bare parameters is determined explicitly, which turns out to depend on the genus 0 sector only. The running coupling constant is also computed exactly, which decreases more rapidly than predicted by the one-loop beta function. A phase transition to an unstable phase is found.