  We study WZW models with the large N=4 superconformal symetry. Our main
result is a geometric interpretation of the large N=4 index. In particular, we
find that states contributing to the index belong to spectral flow orbits of
special RR ground states. We use (anti-)holomorphic differentials with torsion
to clarify the geometric meaning of these states in terms of differential forms
on the target space.
