Toric bases for 6D F-theory models

Abstract

We find all smooth toric bases that support elliptically fiber ed Calabi-Yau threefolds, using the intersection structure of the irredu cible effective divisors on the base. These bases can be used for F-theory constructions of six-di mensional quantum supergrav- ity theories. There are 61,539 distinct possible toric base s. The associated 6D supergravity theories have a number of tensor multiplets ranging from 0 to 193. For each base an explicit Weierstrass parameterization can be determined i n terms of the toric data. The toric counting of parameters matches with the gravitationa l anomaly constraint on mass- less fields. For bases associated with theories having a larg e number of tensor multiplets, there is a large non-Higgsable gauge group containing multi ple irreducible gauge group fac- tors, particularly those having algebras e₈, f₄, and g₂ ⊕ su (2) with minimal (non-Higgsable) matter.