Eur. Phys. J. C (2007) 50: 661-671
https://doi.org/10.1140/epjc/s10052-007-0211-0

Regular Article - Theoretical Physics

Two- and three-loop beta function of non-commutative Φ⁴ ₄ theory

¹ Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Université de Rouen, 76801, Rouen, France
² Laboratoire de Physique Théorique, UMR CNRS 8627, Université Paris-Sud XI, 91405, Orsay, France

^* e-mail: rivass@th.u-psud.fr

Received: 20 October 2006
Published online: 13 February 2007

Abstract

The simplest non-commutative renormalizable field theory, the φ₄ ⁴ model on four dimensional Moyal space with harmonic potential, is asymptotically safe at one loop, as shown by Grosse and Wulkenhaar. We extend this result up to three loops. If this remains true at any loop, it should allow for a full non-perturbative construction of this model.