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

TL;DR

This paper constructs a novel 6D supergravity theory via F-theory on a Calabi-Yau 3-fold with Mordell-Weil torsion, exploring charge completeness, gauge groups, and dualities in string theory.

Contribution

It introduces a new 6D F-theory model with Mordell-Weil torsion $\

Findings

Constructed a 6D supergravity theory with Mordell-Weil torsion $\

Analyzed gauge group and matter content in the F-theory model

Discussed relations to stable degeneration and heterotic duals

Abstract

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.