Building GUTs from strings

TL;DR

This paper develops new techniques for constructing string-derived Grand Unified Theories (GUTs) from orbifold models, leading to novel classes of SO(10) and SU(5) GUTs with specific Higgs content and restrictive properties.

Contribution

It introduces methods for building level-two symmetric orbifold theories and constructs new GUT models, revealing constraints on Higgs representations and couplings in string-derived GUTs.

Findings

Constructed SO(10) GUTs with 45 or 54 Higgs in untwisted sectors

Found SU(5) models with similar restrictions

Identified selection rules forbidding certain GUT-Higgs couplings

Abstract

We study in detail the structure of Grand Unified Theories derived as the low-energy limit of orbifold four-dimensional strings. To this aim, new techniques for building level-two symmetric orbifold theories are presented. New classes of GUTs in the context of symmetric orbifolds are then constructed. The method of permutation modding is further explored and SO(10) GUTs with both $45$ or $54$-plets are obtained. SU(5) models are also found through this method. It is shown that, in the context of symmetric orbifold $SO(10)$ GUTs, only a single GUT-Higgs, either a $54$ or a $45$, can be present and it always resides in an order-two untwisted sector. Very restrictive results also hold in the case of $SU(5)$. General properties and selection rules for string GUTs are described. Some of these selection rules forbid the presence of some particular GUT-Higgs couplings which are sometimes used in SUSY-GUT model building. Some semi-realistic string GUT examples are presented and their properties briefly discussed.