# F-theory models with 3 to 8 U(1) factors on K3 surfaces

## TL;DR

This paper constructs explicit four-dimensional F-theory models with 3 to 8 U(1) gauge factors on K3 surfaces, providing detailed Weierstrass equations and analyzing tadpole cancellation and matter spectra.

## Contribution

It introduces a method to build F-theory models with high Mordell-Weil rank on K3 surfaces using quadratic base change, including explicit equations and flux analysis.

## Key findings

- Explicit Weierstrass equations for K3 surfaces with Mordell-Weil ranks 3 to 8.
- Demonstration of tadpole cancellation in specific Kummer surface pairings.
- Analysis of matter spectra in the constructed F-theory models.

## Abstract

In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations of elliptic K3 surfaces with Mordell-Weil ranks of 3 to 8. We utilize the method of quadratic base change to glue pairs of rational elliptic surfaces together to yield the aforementioned types of K3 surfaces. The moduli of elliptic K3 surfaces constructed in the study include Kummer surfaces of specific complex structures. We show that the tadpole cancels in F-theory compactifications with flux when these Kummer surfaces are paired with appropriately selected attractive K3 surfaces. We determine the matter spectra on F-theory on the pairs.