When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion
We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. Accordingly, we consider complex structure deformations of elliptic fibrations with a Mordell-Weil group of rank one and identify the conditions under which the generating section becomes torsional. In the specific case of Ζ 2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU (2) × SU (4) ]/Ζ 2 × SU (2) . The subsolution with gauge group SU (2) /Ζ 2 × SU (2) , for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Ζ 2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU (2) /Ζ 2 × Ζ 2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.