  Supersymmetric Grand Unified Theories (SGUTs) have achieved some degree of
success, already present in the minimal models (with SU(5) or SO(10)). However,
there are open problems that suggest the need to incorporate more elaborate
constructions, specifically the use of higher-dimensional representations in
the Higgs sector. For example, a $45$ representation of SU(5) is often included
to obtain correct mass relations for the first and second families of d-type
quarks and leptons. When one adds these higher-dimensional Higgs
representations one must verify the cancellation of anomalies associated to
their fermionic partners. One possible choice, free of anomalies, include both
$45,\overline{45}$ representations to cancel anomalies. We review the necessary
conditions for the cancellation of anomalies and discuss the different
possibilities for supersymmetric SU(5) models. Alternative anomaly-free
combinations of Higgs representations, beyond the usual vectorlike choice, are
identified, and it is shown that their corresponding $\beta$ functions are not
equivalent. Although the unification of gauge couplings is not affected, the
introduction of multidimensional representations leads to different scenarios
for the perturbative validity of the theory up to the Planck scale. We study
the effect on the evolution of the gauge coupling up to the Planck scale due to
the different sets of fields and representations that can render an
anomaly-free model.
