We argue that global F-theory compactifications to four dimensions generally
exhibit higher rank Yukawa matrices from multiple geometric contributions known
as Yukawa points. The holomorphic couplings furthermore have large hierarchies
for generic complex structure moduli. Unlike local considerations, the compact
setup realizes these features all through geometry, and requires no instanton
corrections. As an example, we consider a concrete toy model with SU(5)×U(1) gauge symmetry. From the geometry, we find two Yukawa points for the
10−25ˉ65ˉ−4 coupling, producing a rank
two Yukawa matrix. Our methods allow us to track all complex structure
dependencies of the holomorphic couplings and study the ratio numerically. This
reveals hierarchies of O(105) and larger on a full-dimensional
subspace of the moduli space.Comment: 25 pages + appendix and references; v2: matched published version
(typos corrected