Three-family supersymmetric Pati-Salam models with symplectic groups from intersecting D6-branes

We construct new three-family ${\cal N}=1$ supersymmetric Pati-Salam models from intersecting D6-branes with original gauge group ${\rm U}(4)_C \times {\rm USp}(2)_L \times {\rm U}(2)_R$ on a Type IIA $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold. We find that replacing a ${\rm U}(2)$ with a ${\rm USp}(2)$ group severely restricts the number of three-generation supersymmetric models such that there are only five inequivalent models. Exchanging the left and right sectors, we obtain five dual models with gauge group ${\rm U}(4)_C \times {\rm U}(2)_L \times {\rm USp}(2)_R$. These ten models have different gauge coupling relations at string scale. The highest wrapping number is 4, and one of the models contains no filler O6-planes. Moreover, we discuss in detail the particle spectra, the composite particles through strong coupling dynamics, and the exotic particle decouplings. Also, we study how to realize the string-scale gauge coupling relations in some models.