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

Abstract

The simplest non commutative renormalizable field theory, the ${\varphi }_4^4$ 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.

24 pages, 7 figures

Cited by in corpus (17)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• A translation-invariant renormalizable non-commutative scalar model
• Vacuum configurations for renormalizable non-commutative scalar models
• Translation-invariant models for non-commutative gauge fields
• On the vacuum states for noncommutative gauge theory
• Progress in solving a noncommutative quantum field theory in four dimensions
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• On the Effective Action of Noncommutative Yang-Mills Theory
• Why Renormalizable NonCommutative Quantum Field Theories?
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory