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

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.