  We investigate gauge theories and matter fields in F-theory compactifications
on genus-one fibered Calabi-Yau 4-folds without a global section. In this
study, genus-one fibered Calabi-Yau 4-folds are built as direct products of a
genus-one fibered K3 surface that lacks a section times a K3 surface. We
consider i) double covers of $\mathbb{P}^1\times\mathbb{P}^1$ ramified along a
bidegree (4,4) curve, and ii) complete intersections of two bidegree (1,2)
hypersurfaces in $\mathbb{P}^1\times\mathbb{P}^3$ to construct genus-one
fibered K3 surfaces without a section. $E_7$ gauge group arises in some
F-theory compactifications on double covers times K3. We show that the tadpole
can be cancelled for an F-theory compactification on complete intersection K3
times K3, when complete intersection K3 is isomorphic to the Fermat quartic,
and the complex structure of the other K3 surface in the direct product is
appropriately chosen.

High Energy Physics - Theory