Is there a true model-D critical dynamics?

We show that non-locality in the conservation of both the order parameter and a non-critical density (model-D dynamics) leads to new fixed points for critical dynamics. Depending upon the parameters characterizing the non-locality in the two fields, we find four regions: (i) model-A-like, where both conservations are irrelevant; (ii) model-B-like, with the conservation in the order parameter field relevant and the conservation in the coupling field irrelevant; (iii) model-C-like, where the conservation in the order parameter field is irrelevant but the conservation in the coupling field is relevant; and (iv) model-D-like, where both conservations are relevant. While the first three behaviours are already known in dynamical critical phenomena, the last one is a novel phenomenon due entirely to the non-locality in the two fields