Heterotic-type II duality in twistor space

Abstract

Heterotic string theory compactified on a K3 surface times T 2 is believed to beequivalent 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 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 classical 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. © 2013 SISSA.