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

TL;DR

This paper explores the construction of supersymmetric trinification models in Type IIA string theory with intersecting D6-branes, identifying specific models that satisfy complex consistency conditions and detailing their spectra and gauge relations.

Contribution

It systematically searches for consistent four-family models with low wrapping numbers, providing explicit spectra and gauge coupling relations, advancing model-building in string phenomenology.

Findings

Identified a few four-family models with wrapping number 2.

Provided complete particle spectra for these models.

Analyzed gauge coupling relations at the string scale.

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.