  The Hilbert spaces of supersymmetric systems admit symmetries which are often
related to the topology and geometry of the (target) field-space. Here, we
study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are
closely related to superstring models. They all turn out to posess some
hitherto unexploited and geometrically and topologically unobstructed
symmetries, providing new tools for studying the topology and geometry of
superstring target spacetimes, and so the dynamics of the effective field
theory in these.
