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In this paper we prove that the Grosse-Wulkenhaar type non-commutativeorientable complex scalar $\phi^6_3$ theory, with two non-commutativecoordinates and the third one commuting with the other two, is renormalizableto all orders in perturbation theory. Our proof relies on a multiscale analysisin x space.

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