F-theory duals of singular heterotic K3 mode

Abstract

We study F-theory duals of singular heterotic K3 models that correspond to abelian toroidal orbifolds $T^4/Z_N$. While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type $I_0^{\ast },I{V}^{\ast },II{I}^{\ast }$, and $I{I}^{\ast }$. This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi-Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences to our case. Our results show explicitly how the various orbifold models are connected and described in F-theory.

arXiv comment26 pages, 9 figures, 4 tables

References in corpus (29)

• Heterotic and Type I String Dynamics from Eleven Dimensions
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Geometric Singularities and Enhanced Gauge Symmetries
• F-theory and Orientifolds
• Comments on String Dynamics in Six Dimensions
• Vector Bundles And F Theory
• A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
• Supersymmetric Standard Model from the Heterotic String
• Toroidal Compactification Without Vector Structure
• F-Theory at Constant Coupling
• BPS States of Exceptional Non-Critical Strings
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Anomaly Cancellation in Six Dimensions
• Global aspects of the space of 6D N = 1 supergravities
• Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z_6 orbifold
• Point-like Instantons on K3 Orbifolds
• Supersymmetric Standard Model from the Heterotic String (II)
• A unique Z_4^R symmetry for the MSSM
• A Z2xZ2 standard model
• Mapping 6D N = 1 supergravities to F-theory
• Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves
• F-theory on Genus-One Fibrations
• Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles
• Gauged Linear Sigma Models for toroidal orbifold resolutions
• Compact heterotic orbifolds in blow-up
• Weierstrass meets Enriques

Cited by in corpus (7)

• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
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• Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
• Non-Simply-Connected Symmetries in 6D SCFTs
• The Toric SO(10) F-Theory Landscape
• NS5-Branes and Line Bundles in Heterotic/F-Theory Duality
• de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications