  The chiral equivariant cohomology contains and generalizes the classical
equivariant cohomology of a manifold M with an action of a compact Lie group G.
For any simple G, there exist compact manifolds with the same classical
equivariant cohomology, which can be distinguished by this invariant. When M is
a point, this cohomology is an interesting conformal vertex algebra whose
structure is still mysterious. In this paper, we scratch the surface of this
object in the case G=SU(2).
