F-theory Models without Section on Calabi-Yau 4-folds

Research paper by Yusuke Kimura

Indexed on: 11 Jul '16Published on: 11 Jul '16Published in: High Energy Physics - Theory


We consider F-theory models compactified on genus-one fibered Calabi-Yau 4-folds without a section to the fibrations. Therefore, the gauge groups on the 7-branes of such F-theory models do no have $U(1)$-part. We consider two families of genus-one fibered Calabi-Yau 4-folds: i)hypersurface of multidegree (3,2,2,2) in $\mathbb{P}^2\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$, and ii)double cover of $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$ branched along multidegree (4,4,4,4) 3-fold. By construction, these Calabi-Yau 4-folds have genus-one fibrations. We give explicit equations for these families of Calabi-Yau 4-folds, and confirm that the spaces given by the equations do not admit a section to the fibration. The irreducible components of the discriminant loci of the Calabi-Yau 4-folds we consider in this paper intersect with one another. So, 7-branes wrapped on distinct components intersect with one another, and matters localise along these matter curves. We determine the forms of the discriminant components from the defining equations of genus-one fibered Calabi-Yau 4-folds. We then determine the fiber types on the discriminant components. From the fiber types, we obtain the gauge groups on the 7-branes wrapped on the components. For some component, the gauge group enhances when the component coincides with other components so 7-branes wrapped on them become coincident. Gauge groups $E_6$ and $E_7$ appear for some enhanced cases. We determine the potential matter spectra on the bulk, and matters localised along matter curves. We also determine Yukawa couplings which result from the interaction of a matter field on the bulk and two matter fields localised along a matter curve. We compute the generations of chiral matters on the bulk, and matters localised along a matter curve.