$\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s

TL;DR

This paper introduces 1/2 Calabi-Yau 3-folds, a new class of rational elliptic 3-folds, and constructs elliptically fibered Calabi-Yau 3-folds with various Mordell-Weil ranks, advancing F-theory model building.

Contribution

It presents a novel construction method for Calabi-Yau 3-folds using 1/2 Calabi-Yau 3-folds, generalizing the gluing of 1/2 K3 surfaces, and explores F-theory implications.

Findings

Constructed Calabi-Yau 3-folds with multiple U(1) symmetries

Realized models with up to seven tensor multiplets

Established a new geometric approach for F-theory compactifications

Abstract

In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as "1/2 Calabi-Yau 3-folds". We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields a novel approach to build elliptically fibered Calabi-Yau 3-folds of various Mordell-Weil ranks. Our construction of Calabi-Yau 3-folds can be considered as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to seven $U(1)$s form in six-dimensional $N=1$ F-theory on the constructed Calabi-Yau 3-folds. Seven tensor multiplets arise in these models.