Non-Geometric F-Theory-Heterotic Duality

Abstract

In this work we study the duality between F-theory and the heterotic string beyond the stable degeneration limit in F-theory and large fiber limit in the heterotic theory. Building upon a recent proposal by Clingher-Doran and Malmendier-Morrison, which phrases the duality on the heterotic side for a particular class of models in terms of (fibered) genus two curves as non-geometric heterotic compactifications - we establish the precise limit to the semi-classical heterotic string in both eight and lower space-time dimensions. In particular for six dimensional theories, we argue that this class of non-geometric heterotic compactifications capture alpha'-quantum corrections to the semi-classical heterotic supergravity compactifications on elliptically fibered K3 surfaces. From the non-geometric heterotic theory, the semi-classical phase on the K3 surface is recovered from a remarkable limit of genus two Siegel modular forms combined with a geometric surgery operation. Finally, in four dimensions we analyze another limit deep in the quantum regime of the non-geometric heterotic string, which we refer to as the heterotic Sen limit. In this limit we can explicitly argue that the semi-classical two-staged fibrational structure of the heterotic hypermultiplet moduli space - recently established by Alexandrov, Louis, Pioline and Valandro - gets corrected by quantum effects.