Jacobian Calabi--Yau 3-fold and charge completeness in six-dimensional theory

We study aspects of an equivalent relation of the charge completeness in six-dimensional (6D) $\mathcal{N}=(1,0)$ supergravity theory and a standard assumption on the global structure of the gauge group involving F-theory geometry, recently proved by Morrison and Taylor. We constructed and analyzed a novel 6D supergravity theory, realized as F-theory, on an elliptically fibered Calabi--Yau 3-fold. Our construction yields a novel 6D theory with Mordell--Weil torsion $\mathbb{Z}_4\oplus\mathbb{Z}_4$. Furthermore, we deduce the gauge group and matter fields arising in the 6D F-theory model on the constructed elliptically fibered Calabi--Yau 3-fold. We also discuss the relations of the 6D F-theory model constructed in this study to stable degeneration and the dual heterotic string.