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Abstract: Supersymmetric Grand Unified Theories SGUTs have achieved some degree ofsuccess, already present in the minimal models with SU5 or SO10. However,there are open problems that suggest the need to incorporate more elaborateconstructions, specifically the use of higher-dimensional representations inthe Higgs sector. For example, a $45$ representation of SU5 is often includedto obtain correct mass relations for the first and second families of d-typequarks and leptons. When one adds these higher-dimensional Higgsrepresentations one must verify the cancellation of anomalies associated totheir fermionic partners. One possible choice, free of anomalies, include both$45,\overline{45}$ representations to cancel anomalies. We review the necessaryconditions for the cancellation of anomalies and discuss the differentpossibilities for supersymmetric SU5 models. Alternative anomaly-freecombinations of Higgs representations, beyond the usual vectorlike choice, areidentified, and it is shown that their corresponding $\beta$ functions are notequivalent. Although the unification of gauge couplings is not affected, theintroduction of multidimensional representations leads to different scenariosfor the perturbative validity of the theory up to the Planck scale. We studythe effect on the evolution of the gauge coupling up to the Planck scale due tothe different sets of fields and representations that can render ananomaly-free model.

Author: Alfredo Aranda, J. L. Diaz-Cruz, Alma D. Rojas

Source: https://arxiv.org/

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