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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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24 pages, 7 figures

Scientific paper

10.1140/epjc/s10052-007-0211-0

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.

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