F-theory on tetrahedron
DOI:
https://doi.org/10.34874/IMIST.PRSM/fsejournal-v1i1.26792Keywords:
F-theory on Calabi-Yau 4-folds, del Pezzo surfaces, BHV model, Intersecting Branes, Toric singularitesAbstract
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 trifields couplings needed for the engineering of F- theory GUT models building.
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