Commutative limit of a renormalizable noncommutative model

Understand

Renormalizable $\phi^{\star 4}_4$ models on Moyal space have been obtained by modifying the commutative propagator.

• But these models have a divergent "naive" commutative limit.
• We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model.
• The mechanism relies on the analysis of the uv/ir mixing in general Feynman graphs.