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

Kimura, Yusuke

doi:10.1007/jhep02(2020)076

J. High Energ. Phys.

2020

DOI: 10.1007/jhep02(2020)076

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

Yusuke Kimura

Abstract: 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 making use of these rational elliptic 3-folds. This 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 regarded as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to … Show more

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Cited by 3 publications

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Orders of vanishing and U(1) charges in F-theory

Raghuram

Turner

2022

J. High Energ. Phys.

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Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange [1]. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland.

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Orders of vanishing and U(1) charges in F-theory

Raghuram

Turner

2022

J. High Energ. Phys.

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Four-dimensional N = 1 theories, S-fold constraints on T-branes, and behaviors in IR and UV

Kimura

2021

J. High Energ. Phys.

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We analyze four-dimensional (4d) N = 1 superconformal field theories (SCFTs) obtained as deformations of 4d N = 2 SCFTs on S-folds by tilting 7-branes. Geometric compatibility with the structures of S-folds constrains the forms of T-branes. As a result, brane monodromies are constrained. We also discuss two 4d N = 1 theories on probe D3-branes, where the two theories behave identically in IR, but they originate from different theories in UV. Studying the global structure of their geometry is useful in constructing these two theories.

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Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds

Kimura¹

2021

Int. J. Mod. Phys. A

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In this paper, we analyze gauge groups in six-dimensional [Formula: see text] F-theory models. We construct elliptic Calabi–Yau 3-folds possessing various singularity types as double covers of “1/2 Calabi–Yau 3-folds,” a class of rational elliptic 3-folds, by applying the method discussed in a previous study to classify the singularity types of the 1/2 Calabi–Yau 3-folds. One to three U(1) factors are formed in six-dimensional F-theory on the constructed Calabi–Yau 3-folds. The singularity types of the constructed Calabi–Yau 3-folds corresponding to the non-Abelian gauge group factors in six-dimensional F-theory are deduced. The singularity types of the Calabi–Yau 3-folds constructed in this work consist of [Formula: see text]- and [Formula: see text]-type singularities.

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

Cited by 3 publications

References 105 publications

Orders of vanishing and U(1) charges in F-theory

Orders of vanishing and U(1) charges in F-theory

Four-dimensional N = 1 theories, S-fold constraints on T-branes, and behaviors in IR and UV

Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds

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