Anomalies, Beta Functions and Supersymmetric Unification with Multi-Dimensional Higgs Representations

TL;DR

This paper explores how extending supersymmetric GUT models with multi-dimensional Higgs representations affects anomaly cancellation and gauge coupling unification, revealing new anomaly-free configurations and their impact on theory validity.

Contribution

It identifies alternative anomaly-free Higgs representation combinations in SUSY SU(5) models and analyzes their effects on beta functions and unification scenarios.

Findings

Alternative anomaly-free Higgs combinations found

Beta functions differ among these combinations

Gauge coupling unification remains unaffected

Abstract

In the framework of supersymmetric Grand Unified Theories, the minimal Higgs sector is often extended by introducing multi-dimensional Higgs representations in order to obtain realistic models. However these constructions should remain anomaly-free, which constraints significantly their structure. We review the necessary conditions for the cancellation of anomalies in general and discuss in detail the different possibilities for SUSY SU(5) models. Alternative anomaly free combinations of Higgs representations, beyond the usual vector-like 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 multi-dimensional representations leads to different scenarios for the perturbative validity of the theory up to the Planck scale.