Grand-unification Theory Atlas: Standard Model and Beyond

TL;DR

This paper constructs a comprehensive atlas of simple gauge theories, identifying minimal grand-unification models and exploring extensions beyond the Standard Model using a gauge-invariance and degrees-of-freedom framework.

Contribution

It introduces a novel atlas-based approach to classify gauge theories and identifies the SU(5) and SO(10) models as minimal grand-unification candidates under specific assumptions.

Findings

SU(5) is the minimal GUT model based on free energy analysis.

SO(10) with spinorial matter closely follows SU(5) in minimality.

The atlas delineates the landscape of grand-unifiable gauge extensions of the Standard Model.

Abstract

Under a reasonable set of ab-initio assumptions, we define and chart the atlas of simple gauge theories with families of fermions whose masses are forbidden by gauge invariance. We propose a compass to navigate the atlas based on counting degrees of freedom. When searching for Grand-unification Theories with three matter generations, the free energy singles out the SU(5) Georgi-Glashow model as the minimal one, closely followed by SO(10) with spinorial matter. The atlas also defines the dryland of grand-unifiable gauge extensions of the standard model. We further provide examples relevant for gauge dual completions of the standard model as well as extensions by an additional SU(N) gauge symmetry.