Unitarity constraints on large multiplets of arbitrary gauge groups

TL;DR

This paper derives unitarity constraints on large multiplets in arbitrary gauge groups, impacting the viability of certain GUT models and their perturbative consistency.

Contribution

It provides a general method to impose unitarity bounds on large multiplets across arbitrary gauge groups, extending previous analyses.

Findings

Certain GUT scenarios violate unitarity bounds

Constraints on scalar and fermionic multiplet sizes

Implications for perturbative validity in GUTs

Abstract

We impose partial-wave unitarity on $2 \to 2$ tree-level scattering processes to derive constraints on the dimensions of large scalar and fermionic multiplets of arbitrary gauge groups. We apply our results to scalar and fermionic extensions of the Standard Model, and also to the Grand Unified Theories (GUTs) based on the groups $SU(5)$, $SO(10)$, and $E_6$. We find scenarios within the latter two GUTs that violate the unitarity condition; this may require a reevaluation of the validity of perturbation theory in those scenarios.