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We consider noncommutative GUT inspired field theories formulated within theenveloping-algebra formalism for anomaly safe compact simple gauge groups. Ourtheories have only gauge fields and fermions, and we compute the UV divergentpart of the one-loop background-field effective action involving two fermionicfields at first order in the noncommutativity parameter theta. We show that, ifthe second-degree Casimir has the same value for all the irreps furnished bythe fermionic multiplets of the model, then, that UV divergent part can berenormalised by carrying out multiplicative renormalisations of the couplingconstant, theta and the fields, along with the inclusion of theta-dependentcounterterms which vanish upon imposing the equations of motion. Thesetheta-dependent counterterms have no physical effect since they vanishon-shell. This result along with the vanishing of the UV divergent part of thefermionic four-point functions leads to the unexpected conclusion that theone-loop matter sector of the background-field effective action of thesetheories is one-loop multiplicatively renormalisable on-shell. We also showthat the background-field effective action of the gauge sector of the theoriesconsidered here receives no theta-dependent UV divergent contributions atone-loop. We thus conclude that these theories are on-shell one-loopmultiplicatively renormalisable at first order in theta.

Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups