Renormalization of Orientable Non-Commutative Complex $Φ^6_3$ Model

In this paper we prove that the Grosse-Wulkenhaar type non-commutative orientable complex scalar $ϕ^6_3$ theory, with two non-commutative coordinates and the third one commuting with the other two, is renormalizable to all orders in perturbation theory. Our proof relies on a multiscale analysis in x space.

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