A nontrivial solvable noncommutative \phi^3 model in 4 dimensions

TL;DR

This paper demonstrates that a noncommutative  model in 4D can be quantized and made renormalizable by mapping it to a Kontsevich model, revealing a nontrivial interacting quantum field theory in four dimensions.

Contribution

The authors establish the renormalizability of a 4D noncommutative  model via a Kontsevich model mapping, including the necessary counterterm and analysis of stability.

Findings

Model is renormalizable with an additional counterterm.

Genus expansion of free energy and n-point functions is finite after renormalization.

Identifies a critical coupling beyond which the model becomes unstable.

Abstract

We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the 2-dimensional case which can be interpreted as divergent shift of the field \phi. The known results for the Kontsevich model allow to obtain the genus expansion of the free energy and of any n-point function, which is finite for each genus after renormalization. No coupling constant or wavefunction renormalization is required. A critical coupling is determined, beyond which the model is unstable. This provides a nontrivial interacting NC field theory in 4 dimensions.