Two and Three Loops Beta Function of Non Commutative $\Phi^4_4$ Theory

TL;DR

This paper extends the analysis of the non-commutative $\

Contribution

It computes the beta function of the $\

Findings

Beta function calculated up to three loops

Supports asymptotic safety of the model

Potential for non-perturbative construction

Abstract

The simplest non commutative renormalizable field theory, the $\phi_4^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this result up to three loops. If this remains true at any loop, it should allow a full non perturbative construction of this model.