  For any algebraic super-manifold M we define the super-ind-scheme LM of
formal loops and study the transgression map (Radon transform) on differential
forms in this context. Applying this to the super-manifold M=SX, the spectrum
of the de Rham complex of a manifold X, we obtain, in particular, that the
transgression map for X is a quasi-isomorphism between the [2,3)-truncated de
Rham complex of X and the additive part of the [1,2)-truncated de Rham complex
of LX. The proof uses the super-manifold SSX and the action of the Lie
superalgebra sl(1|2) on this manifold. This quasi-isomorphism result provides a
crucial step in the classification of sheaves of chiral differential operators
in terms of geometry of the formal loop space.
