Renormalization of the noncommutative phi^3 model through the Kontsevich model

TL;DR

This paper demonstrates how the noncommutative phi^3 model can be mapped to the Kontsevich model, enabling the use of its known results for nonperturbative analysis, renormalization, and stability in quantum field theory.

Contribution

It establishes a mapping between the noncommutative phi^3 model and the Kontsevich model, providing explicit nonperturbative solutions and renormalization results.

Findings

Full renormalization at finite coupling is achieved, determined by genus 0 sector.

All contributions in the genus expansion are finite after renormalization.

Identifies a critical coupling beyond which the model becomes unstable.

Abstract

We point out that the noncommutative selfdual phi^3 model can be mapped to the Kontsevich model, for a suitable choice of the eigenvalues in the latter. This allows to apply known results for the Kontsevich model to the quantization of the field theory, in particular the KdV flows and Virasoro constraints. The 2-dimensional case is worked out explicitly. We obtain nonperturbative expressions for the genus expansion of the free energy and some n-point functions. The full renormalization for finite coupling is found, which is determined by the genus 0 sector only. All contributions in a genus expansion of any n-point function are finite after renormalization. A critical coupling is determined beyond which the model is unstable. The model is free of UV/IR diseases.