Toric bases for 6D F-theory models

TL;DR

This paper systematically classifies all smooth toric bases for elliptically fibered Calabi-Yau threefolds, enabling the construction of 6D F-theory models and matching geometric parameters with physical anomaly constraints.

Contribution

It provides a complete enumeration of 61,539 toric bases for 6D F-theory models and explicitly constructs their Weierstrass models from toric data.

Findings

Identified all smooth toric bases supporting elliptic Calabi-Yau threefolds.

Matched geometric parameters with gravitational anomaly constraints.

Found large non-Higgsable gauge groups with specific algebraic structures.

Abstract

We find all smooth toric bases that support elliptically fibered Calabi-Yau threefolds, using the intersection structure of the irreducible effective divisors on the base. These bases can be used for F-theory constructions of six-dimensional quantum supergravity theories. There are 61,539 distinct possible toric bases. 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 in terms of the toric data. The toric counting of parameters matches with the gravitational anomaly constraint on massless fields. For bases associated with theories having a large number of tensor multiplets, there is a large non-Higgsable gauge group containing multiple irreducible gauge group factors, particularly those having algebras e_8, f_4 and (g_2 + su(2)) with minimal (non-Higgsable) matter.