Orientifolds for F-theory on K3 Surfaces

TL;DR

This paper explores F-theory orientifolds on K3 surfaces, analyzing their complex geometry, real structures, and physical implications, including charge spectra and degenerations to isotrivial fibrations.

Contribution

It introduces a new family of lattice-polarized K3 surfaces for F-theory orientifolds, extending previous models and analyzing their geometric and physical properties.

Findings

Characterized the complex geometry of the K3 family.

Analyzed real structures and their effects on the charge spectrum.

Described degenerations to isotrivial Kummer surface fibrations.

Abstract

We study F-theory orientifolds, starting with products of two elliptic curves, but focusing mostly on a family of K3 surfaces, lattice polarized by the rank-17 lattice $\langle 8 \rangle \oplus 2D_8(-1)$, generalizing the family (to which it degenerates) of Kummer surfaces of products of two non-isogenous elliptic curves. After a thorough study of the complex geometry of this family and its elliptic fibrations, we proceed to study real structures on the K3 surfaces in the family which are equivariant with respect to an elliptic fibration. We also study the physics of the associated F-theory orientifolds with a particular focus on the impact of the real structure on the charge spectrum. We also study how these orientifolds degenerate to the case of isotrivial Kummer surface fibrations.