  We consider the GUT compatible formulation of noncommutative QED, as well as
noncommutative SU(N) GUTs, for N>2, with no scalars but with fermionic matter
in an arbitrary, anomaly-free representation, in the enveloping algebra
approach. We compute, to first order in the noncommutativity parameters theta,
the UV divergent part of the one-loop background-field effective action
involving at most two fermion fields and an arbitrary number of gauge fields.
It turns out that, for special choices of the ambiguous trace over the gauge
degrees of freedom, for which the O(theta) triple gauge-field interactions
vanish, the divergences can be absorbed by means of multiplicative
renormalisations and the inclusion of theta-dependent counterterms that vanish
on-shell and are thus unphysical. For this to happen in the SU(N), N>2 case,
the representations of the matter fields must have a common second Casimir;
anomaly cancellation then requires the ordinary (commutative) matter content to
be non-chiral. Together with the vanishing of the divergences of fermionic four
point functions, this shows that GUT inspired theories with U(1) and SU(N), N>2
gauge groups and ordinary vector matter content not only have a renormalisable
matter sector, but are on-shell one-loop multiplicatively renormalisable at
order one in theta.
