The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines

Abstract

We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank $16$. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3 surfaces and express their parameters in terms of modular forms generalizing Siegel modular forms. In this way, we find a complete list of all dual non-geometric compactifications obtained by the partial higgsing of the heterotic string gauge algebra using two Wilson line parameters.

arXiv comment22 pages. arXiv admin note: substantial text overlap with arXiv:1908.09578, arXiv:1806.07460

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• On two-elementary K3 surfaces with finite automorphism group
• K3 Surfaces and Orthogonal Modular Forms
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence
• New perspectives in the duality of M-theory, heterotic strings, and F-theory
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups