Non-split singularities and conifold transitions in F-theory

TL;DR

This paper explores the relationship between split and non-split singular fibers in F-theory, showing they correspond to conifold transitions and analyzing the emergence of non-local matter through blow-up techniques.

Contribution

It demonstrates that split/non-split transitions are conifold transitions in F-theory and clarifies the geometric origin of non-local matter in these models.

Findings

Split/non-split transitions correspond to conifold transitions.

Non-local matter arises from conifold singularities.

Analysis applies to models with $D_{2k+2}$ and $E_7$ singularities.

Abstract

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 $D_{2k+2}$ $(k \geq 1)$ or $E_7$. We also examine how the previous proposal for the origin of non-local matter can be actually implemented in our blow-up analysis.