String GUTs

TL;DR

This work investigates embedding SUSY-GUTs within four-dimensional string theory by realizing grand-unified groups such as $SU(5)$ and $SO(10)$ at level $k=2$ via higher-level orbifolds on the Spin(32)/Z2 lattice. It develops and analyzes three construction strategies—continuous Wilson lines, permutation modding, and Higgs-induced flat directions—to generate diagonal GUTs and GUT-Higgs fields that often arise as string moduli with limited self-couplings. A recurring feature is a single $54$ (for $SO(10)$) or analogous GUT-Higgs in the untwisted sector, plus extra matter that generally shifts gauge coupling unification, potentially requiring intermediate scales and invoking Fayet–Iliopoulos terms for vacuum stabilization. The study highlights both the prospects and challenges of string-GUTs, including doublet-triplet splitting considerations and the need for extending to asymmetric orbifolds and three-generation models to achieve MSSM-like low-energy physics. Overall, it provides concrete constructions and phenomenological insights toward a string-theoretic realization of GUTs within a quantum-gravity-consistent framework.

Abstract

Standard SUSY-GUTs such as those based on $SU(5)$ or $SO(10)$ lead to predictions for the values of $α_s$ and $sin^2θ_W$ in amazing agreement with experiment. In this article we investigate how these models may be obtained from string theory, thus bringing them into the only known consistent framework for quantum gravity. String models with matter in standard GUT representations require the realization of affine Lie algebras at higher levels. We start by describing some methods to build level $k=2$ orbifold string models with gauge groups $SU(5)$ or $SO(10)$. We present several examples and identify generic features of the type of models constructed. Chiral fields appropriate to break the symmetry down to the standard model generically appear in the massless spectrum. However, unlike in standard SUSY-GUTs, they often behave as string moduli, i.e., they do not have self-couplings. We also discuss briefly the doublet-triplet Higgs splitting. We find that, in some models, built-in sliding-singlet type of couplings exist.