Revisiting the $\mathcal{N}=1$ supersymmetric trinification models from intersecting D6-branes

Abstract

We revisit the construction of the $\mathcal{N}=1$ supersymmetric trinification models with gauge group $\mathrm{U}(3{)}_C\times \mathrm{U}(3{)}_L\times \mathrm{U}(3{)}_R$ in Type IIA string theory on ${\mathbf{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold with intersecting D6-branes. The non-trivial K-theory conditions and tadpole cancellation conditions severely restrict the number of allowed models even for the case of rectangular two-tori. Using a supervised search algorithm, we find a few four-family models where the highest wrapping number is 2. For these models, we present the complete particle spectra and the gauge coupling relations at the string-scale.

Comments: 18 pages, accepted in CTP. arXiv admin note: substantial text overlap with arXiv:2212.09644, arXiv:2303.02864