Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

Understand

We consider noncommutative gauge theory defined by means of Seiberg-Witten maps for an arbitrary semisimple gauge group.

• We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters $\theta$.
• We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group.
• We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg-Witten maps that are linear in the matter fields.