Quiver Gauge Models in F-Theory on Local Tetrahedron

Abstract

We study a class of 4D $\mathcal{N}=1$ supersymmetric GUT- type models in the framework of the Beasley-Heckman-Vafa theory. We first review general results on MSSM and supersymmetric GUT; and we describe useful tools on 4D quiver gauge theories in F- theory set up. Then we study the effective supersymmetric gauge theory in the 7-brane wrapping 4-cycles in F-theory on local elliptic CY4s based on a complex tetrahedral surface $\mathcal{T}$ and its blown ups ${\mathcal{T}}_n$. The complex 2d geometries $\mathcal{T}$ and ${\mathcal{T}}_n$ are \emph{non planar} projective surfaces that extend the projective plane ${\mathbb{P}}^2$ and the del Pezzos. Using the power of toric geometry encoding the toric data of the base of the local CY4, we build a class of \emph{4D} $\mathcal{N}=1$ non minimal GUT- type models based on $\mathcal{T}$ and ${\mathcal{T}}_n$. An explicit construction is given for the SU$(5)$ GUT-type model.

86 pages, 20 figures

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