Tetrahedron in F-theory Compactification

Abstract

Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface that is generated by four intersecting complex projective planes $C{P}^2$. In this paper, we study the family $\{{\mathcal{T}}_m\}$ of blow ups of $\mathcal{T}$ and exhibit the link of these ${\mathcal{T}}_m$s with the set of del Pezzo surfaces $d{P}_n$ obtained by blowing up n isolated points in the $C{P}^2$. The ${\mathcal{T}}_m$s are toric surfaces exhibiting a $U(1)\times U(1)$ 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.

27 pages, 9 figures

References in corpus (5)

• The $G_2$-MSSM - An $M$ Theory motivated model of Particle Physics
• Gauge Mediation in F-Theory GUT Models
• F-Theory, GUTs and Chiral Matter
• Geometric Transitions, del Pezzo Surfaces and Open String Instantons
• Connecting String/M Theory to the Electroweak Scale and to LHC Data

Cited by in corpus (1)

• Quiver Gauge Models in F-Theory on Local Tetrahedron