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A note on transition in discrete gauge groups in F-theory

We observe a new puzzling physical phenomenon in F-theory on the multisection geometry, wherein a model without a gauge group transitions to another model with a discrete $\mathbb{Z}_n$ gauge group via Higgsing. This phenomenon may suggest an unknown aspect of F-theory compactification on multisection geometry lacking a global section. A possible interpretation of this puzzling physical phenomenon is proposed in this note. We also propose a possible interpretation of another unnatural physical phenomenon observed for F-theory on four-section geometry, wherein a discrete $\mathbb{Z}_2$ gauge group transitions to a discrete $\mathbb{Z}_4$ gauge group via Higgsing as described in the previous literature.