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We investigate gauge theories and matter contents in F-theorycompactifications on families of genus-one fibered Calabi-Yau 4-folds lacking aglobal section. To construct families of genus-one fibered Calabi-Yau 4-foldsthat lack a global section, we consider two constructions: hypersurfaces in aproduct of projective spaces, and double covers of a product of projectivespaces. We consider specific forms of defining equations for these genus-onefibrations, so that genus-one fibers possess complex multiplications ofspecific orders. These symmetries enable a detailed analysis of gauge theories.$E_6$, $E_7$, and $SU(5)$ gauge groups arise in some models. Discriminantcomponents intersect with one another in the constructed models, and therefore,discriminant components contain matter curves. We deduce potential matterspectra and Yukawa couplings.

advances in theoretical and mathematical physics

Gauge groups and matter spectra in F-theory compactifications on  genus-one fibered Calabi-Yau 4-folds without section - hypersurface and  double cover constructions