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I am reading a paper of renormalization of field theory on noncommutative torus. At the end of chapter 6 there is the following statement "Although our analysis is far from being exhaustive, we believe it strongly suggest that the $\varphi^4$ theory on $\mathbb{T}_\theta^4$ is renormalizable." This paper was published in April. Are there some new results in this branch or is it still an open problem ?

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