Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors

Understand

An algorithm to systematically construct all Calabi-Yau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described.

• This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors.
• The basic data consists of a top over each toric divisor in the base together with compactification data giving the embedding into a reflexive polytope.
• The allowed choices of compactification data are integral points in an auxiliary polytope.