Grand Unification with Higher Rank Product Groups

TL;DR

This paper explores the viability of higher-rank product gauge groups like $SU(5) imes SU(5)$ and $SO(10) imes SO(10)$ for grand unification, highlighting constraints from string theory and the GUT scale as a modulus.

Contribution

It demonstrates that $SU(5) imes SU(5)$ models can be constructed with the GUT scale as a modulus, but extending to $SO(10) imes SO(10)$ introduces problematic massless modes, constraining model possibilities.

Findings

$SU(5) imes SU(5)$ models can incorporate the GUT scale as a modulus.

Extending to $SO(10) imes SO(10)$ leads to unwanted massless modes.

Constraints from string theory and the GUT scale as a modulus limit model building options.

Abstract

Various ideas support the notion that the GUT gauge group might be a semi-simple direct-product group such as $SU(5) \times SU(5)$. The doublet-triplet splitting problem can be solved with a direct product group. String theory suggests that the GUT scale is a modulus. Requiring this rules out a single SU(5) gauge group. A model with $SU(5) \times SU(5)$ gauge symmetry and the GUT scale as a modulus has been shown to exist. It is shown that extending these ideas to $SO(10) \times SO(10)$ cannot be done with the above requirement without unwanted massless modes at lower energy scales that spoil the unification of couplings. Therefore these two conditions highly constrain the class of possible GUT models.