Higher-dimensional Higgs Representations in SGUT models

TL;DR

This paper explores the use of higher-dimensional Higgs representations in supersymmetric GUT models, analyzing anomaly cancellation, gauge coupling evolution, and the implications for model validity up to the Planck scale.

Contribution

It identifies alternative anomaly-free Higgs representation combinations in SU(5) SGUTs and examines their impact on gauge coupling evolution and model perturbativity.

Findings

Different anomaly-free Higgs sets lead to distinct beta functions.

Gauge coupling unification remains unaffected by higher-dimensional representations.

Models with multidimensional Higgs fields have varied perturbative validity up to the Planck scale.

Abstract

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.