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Heterotic string theory compactified on a K3 surface times T^2 is believed tobe equivalent to type II string theory on a suitable Calabi-Yau threefold. Inparticular, it must share the same hypermultiplet moduli space. Building on theknown twistorial description on the type II side, and on recent progress on themap between type II and heterotic moduli in the `double scaling' limit (whereboth the type II and heterotic strings become classical), we provide a newtwistorial construction of the hypermultiplet moduli space in this limit whichis adapted to the symmetries of the heterotic string. We also take stepstowards understanding the twistorial description for heterotic worldsheetinstanton corrections away from the double scaling limit. As a spin-off, weobtain a twistorial description of a class of automorphic forms of SO(4,n,Z)obtained by Borcherds' lift.

Heterotic-type II duality in twistor space