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 $(6D) N = (1, 0)$ 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.

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Published 19 August 2024