Non-Geometric F-Theory-Heterotic Duality

TL;DR

This paper explores the duality between F-theory and heterotic string theory beyond traditional limits, revealing how non-geometric heterotic compactifications encode quantum corrections and connect to semi-classical regimes across various dimensions.

Contribution

It establishes the precise limits connecting non-geometric heterotic models to semi-classical heterotic strings, extending duality understanding beyond stable degeneration and large fiber limits.

Findings

Non-geometric heterotic compactifications capture alpha'-quantum corrections.

A limit of genus two Siegel modular forms recovers semi-classical phases.

Quantum effects correct the heterotic hypermultiplet moduli space structure.

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.