Non-split singularities and conifold transitions in F-theory

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 $D_{2k+2}$ $(k\ge 1)$ 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.

arXiv comment38 pages, 7 figures, 2 tables; v3: Added new paragraphs describing the relationship between the work of Aspinwall, Katz and Morrison and the present work. To appear in JHEP

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