Advances in Theoretical and Mathematical Physics

Volume 12 (2008)

Number 3

Exact renormalization of a noncommutative Φ3 model in 6 dimensions

Pages: 605 – 639



Harald Grosse

Harold Steinacker


The noncommutative self-dual φ3 model in six 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 1-loop beta-function. A phase transition to an unstable phase is found.

Published 1 January 2008