  Because 4-dimensional CP is a good symmetry of many higher-dimensional
theories, this suggests the possible existence of a universal CP-violating
phase originating from the process of compactification. Such a phase, if it
existed, would not be easy to uncover since the phases in Yukawa matrices are
not simply related to the observed CKM phase $\delta$. Hierarchical Yukawa
models of the type arising in F-theory GUT models provide an interesting
exception. Recently, Heckman and Vafa studied a particular F-theory GUT model
with hierarchical Yukawa matrices with complex phases of O(1) and showed, by
examining the Jarlskog invariant, that this model leads to $\sin \delta \sim
O(1)$. A more detailed examination of the model, although confirming their
result, is seen to be also compatible with having a phase $\delta_o= \pi/3$
imprinted on the Hermitian Yukawa matrices, leading to $\sin \delta \simeq \sin
\delta_o$.
