Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17

TL;DR

This paper explores the moduli space of elliptic K3 surfaces with specific ADE types, identifying special points where gauge symmetries and Picard numbers are enhanced, with implications for F-theory compactifications.

Contribution

It constructs and analyzes the moduli of K3 surfaces with ADE types E7 D10 and A17, identifying special points with enhanced gauge symmetries and Picard numbers.

Findings

Identification of special points where K3 surfaces become attractive.

Demonstration of U(1) gauge symmetry emergence in F-theory.

Construction of moduli spaces for specific ADE types.

Abstract

We study the moduli of elliptic K3 surfaces with a section with the $ADE$ rank 17. While the Picard number of a generic K3 surface in such moduli space is 19, the Picard number is enhanced to 20 at special points in the moduli. K3 surfaces become attractive K3 surfaces at these points. Either of the following two situations occurs at such special points: i) the Mordell-Weil rank of an elliptic K3 surface is enhanced, or ii) the gauge symmetry is enhanced. The first case i) is related to the appearance of a $U(1)$ gauge symmetry. In this note, we construct the moduli of K3 surfaces with $ADE$ types $E_7 D_{10}$ and $A_{17}$. We determine some of the special points at which K3 surfaces become attractive in the moduli of K3 surfaces with $ADE$ types $E_7 D_{10}$ and $A_{17}$. We investigate the gauge symmetries in F-theory compactifications on attractive K3 surfaces which correspond to such special points in the moduli times a K3 surface. $U(1)$ gauge symmetry arises in some F-theory compactifications.