K3 surfaces, modular forms, and non-geometric heterotic compactifications

Abstract

We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3 surfaces. The modular group mixes together the Kähler, complex structure, and Wilson line moduli of the torus yielding weakly coupled heterotic string compactifications which have no large radius interpretation.

32 pages. v3 has minor changes and additional references

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• c=2 Rational Toroidal Conformal Field Theories via the Gauss Product
• U-folds as K3 fibrations
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Cited by in corpus (43)

• F-theory and the Classification of Little Strings
• Non-geometric backgrounds in string theory
• Siegel modular flavor group and CP from string theory
• Exploring the landscape of heterotic strings on T^d
• TASI Lectures on F-theory
• Physics of Infinite Complex Structure Limits in eight Dimensions
• The Satake sextic in elliptic fibrations on K3
• Type IIB flux vacua from G-theory II
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• Six line configurations and string dualities
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Ubiquity of non-geometry in heterotic compactifications
• The monodromy of T-folds and T-fects
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Supergravity in Twelve Dimension
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
• A Universal Genus-Two Curve from Siegel Modular Forms
• F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
• Kummer sandwiches and Greene-Plesser construction
• Normal forms for Kummer surfaces
• Discrete anomalies in supergravity and consistency of string backgrounds
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories
• A Landscape of Field Theories
• Nikulin involutions and the CHL string
• On K3 surfaces of Picard rank 14
• M-theory on non-Kähler manifolds
• Counting Rational Points on Kummer surfaces
• A note on T-folds and T3 fibrations
• On the mixed-twist construction and monodromy of associated Picard-Fuchs systems
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• On Néron-Severi lattices of Jacobian elliptic K3 surfaces
• On the duality of F-theory and the CHL string in seven dimensions
• A class of non-geometric M-theory compactification backgrounds
• Non-geometric heterotic backgrounds and 6D SCFTs/LSTs
• On effective field theory of F-theory beyond leading order
• Isogenies of certain K3 surfaces of rank 18
• Orbifolds from $\mathrm{Sp}(4,\mathbb{Z})$ and their modular symmetries
• New perspectives in the duality of M-theory, heterotic strings, and F-theory
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence