Heterotic-type II duality in twistor space

TL;DR

This paper develops a twistorial framework for the hypermultiplet moduli space in heterotic-type II duality, focusing on the classical limit and automorphic forms, advancing understanding of string dualities and instanton corrections.

Contribution

It introduces a new twistorial construction of the heterotic hypermultiplet moduli space aligned with heterotic symmetries, extending previous type II descriptions and exploring instanton effects.

Findings

Constructed a twistorial description of the heterotic moduli space in the classical limit.

Linked automorphic forms of SO(4,n,Z) to Borcherds' lift within the twistorial framework.

Provided insights into heterotic worldsheet instanton corrections beyond the double scaling limit.

Abstract

Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the `double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the double scaling limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4,n,Z) obtained by Borcherds' lift.