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We investigate gauge theories and matter fields in F-theory compactificationson genus-one fibered Calabi-Yau 4-folds without a global section. In thisstudy, genus-one fibered Calabi-Yau 4-folds are built as direct products of agenus-one fibered K3 surface that lacks a section times a K3 surface. Weconsider i) double covers of $\mathbb{P}^1\times\mathbb{P}^1$ ramified along abidegree (4,4) curve, and ii) complete intersections of two bidegree (1,2)hypersurfaces in $\mathbb{P}^1\times\mathbb{P}^3$ to construct genus-onefibered K3 surfaces without a section. $E_7$ gauge group arises in someF-theory compactifications on double covers times K3. We show that the tadpolecan be cancelled for an F-theory compactification on complete intersection K3times K3, when complete intersection K3 is isomorphic to the Fermat quartic,and the complex structure of the other K3 surface in the direct product isappropriately chosen.

advances in theoretical and mathematical physics

Gauge symmetries and matter fields in F-theory models without section-  compactifications on double cover and Fermat quartic K3 constructions times  K3