Induced gauge theory on a noncommutative space

We consider a scalar φ⁴ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action, using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.