Abstract
In the framework of supersymmetric grand unified theories, the minimal Higgs sector is often extended by introducing multidimensional Higgs representations in order to obtain realistic models. However these constructions should remain anomaly-free, which significantly constrains their structure. We review the necessary conditions for the cancellation of anomalies in general and discuss in detail 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.
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