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The duality between F-theory and the heterotic string in \(D=8\) with two Wilson lines

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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.

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  1. Department of Mathematics, University of Missouri St. Louis, St. Louis, MO, 63121, USA

    Adrian Clingher

  2. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

    Thomas Hill & Andreas Malmendier

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A.M. acknowledges support from the Simons Foundation through Grant No. 202367.

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Clingher, A., Hill, T. & Malmendier, A. The duality between F-theory and the heterotic string in \(D=8\) with two Wilson lines. Lett Math Phys 110, 3081–3104 (2020). https://doi.org/10.1007/s11005-020-01323-8

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