Grand unfication models from SO(32) heterotic string

TL;DR

This paper constructs grand unification models from SO(32) heterotic string theory using $ ext{Z}_{12-I}$ orbifold compactification, introducing novel anti-SU($N$) models with chiral spectra and anomaly cancellation, relevant for future phenomenological studies.

Contribution

It presents a new class of anti-SU($N$) GUT models from SO(32) heterotic string compactification with chiral spectra and anomaly-free gauge groups, expanding the landscape of string-derived GUTs.

Findings

Constructed SU(9) and SU(5)$'$ GUT models with chiral spectra.

Confirmed non-Abelian anomaly cancellation in the models.

Provided Yukawa couplings for fermion mass generation.

Abstract

Grand unification groups (GUTs) are constructed from SO(32) heterotic string via $\Z_{12-I}$ orbifold compactification. So far, most phenomenological studies from string compactification relied on $\EE8$ heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the anti-symmetric tensor representations of SU($N$). The anti-SU($N$) presented in this paper is a completely different class from the flipped-SU($N$)s from the spinor representations of SO($2N$). Here, we realize chiral representations: $\tsix\oplus 5\cdot\nineb $ for a SU(9) GUT and $3\{{\ten}'_L\oplus {\fiveb}'_L\}$ for a SU(5)$'$ GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, $t$, and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU(5)$'$ GUT.