Tetrahedron in F-theory Compactification
Abstract
Complex tetrahedral surface T is a non planar projective surface that is generated by four intersecting complex projective planes CP2. In this paper, we study the family \Tm\ of blow ups of T and exhibit the link of these Tms with the set of del Pezzo surfaces dPn obtained by blowing up n isolated points in the CP2. The Tms are toric surfaces exhibiting a U(1) × U(1) symmetry that may be used to engineer gauge symmetry enhancements in the Beasley-Heckman-Vafa theory. The blown ups of the tetrahedron have toric graphs with faces, edges and vertices where may localize respectively fields in adjoint representations, chiral matter and Yukawa tri-fields couplings needed for the engineering of F- theory GUT models building.
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