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

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.

27 pages

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Cited by in corpus (16)

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• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
• Extremal 1/2 Calabi-Yau 3-folds and six-dimensional F-theory applications
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• $\frac{1}{2}$Calabi-Yau 4-folds and four-dimensional F-theory on Calabi-Yau 4-folds with U(1) factors
• New perspectives in the duality of M-theory, heterotic strings, and F-theory
• Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory