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

TL;DR

This paper explores non-geometric heterotic string compactifications using F-theory duals and reveals a connection between Siegel modular forms and K3 surface equations, leading to novel moduli mixing.

Contribution

It introduces a new construction of non-geometric heterotic compactifications via F-theory duality and links modular forms to K3 surface equations.

Findings

Moduli mixing occurs through the modular group.

Non-geometric compactifications lack large radius limits.

Connections between Siegel modular forms and K3 surfaces are established.

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 K\"ahler, complex structure, and Wilson line moduli of the torus yielding weakly coupled heterotic string compactifications which have no large radius interpretation.