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

TL;DR

This paper proves the all-order renormalizability of a specific non-commutative complex scalar field theory with mixed commutative and non-commutative coordinates using multiscale analysis.

Contribution

It provides a rigorous proof of renormalizability for a Grosse-Wulkenhaar type non-commutative $\

Findings

Proves renormalizability to all orders in perturbation theory

Uses multiscale analysis in x space

Extends understanding of non-commutative quantum field theories

Abstract

In this paper we prove that the Grosse-Wulkenhaar type non-commutative orientable complex scalar $\phi^6_3$ 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.