Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory

TL;DR

This paper demonstrates that a specific non-commutative quantum field theory, the $$ model on four-dimensional Moyal space with harmonic potential, remains well-behaved at high energies due to its asymptotic safety.

Contribution

It proves the all-order perturbative asymptotic safety of the simplest non-commutative renormalizable field theory with harmonic potential.

Findings

The $$ model is asymptotically safe at all perturbation orders.

The model remains well-defined and free of Landau ghosts.

This work advances understanding of non-commutative quantum field theories.

Abstract

We show that the simplest non commutative renormalizable field theory, the $\phi^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theory