Non-split singularities and conifold transitions in F-theory

In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called “split” or “non-split” type depending on whether it is globally possible or not. In the latter case, the gauge symmetry is reduced to a non-simply-laced Lie algebra due to monodromy. We show that this split/non-split transition is, except for a special class of models, a conifold transition from the resolved to the deformed side, associated with the conifold singularities emerging where the codimension-one singularity is enhanced to D2k+2 (k ≥ 1) or E7. We also examine how the previous proposal for the origin of non-local matter can be actually implemented in our blow-up analysis.