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

Research paper by **Yusuke Kimura**

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

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#### Abstract

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.