  Scattering amplitudes in superconformal field theories do not enjoy this
symmetry, because the definition of asymptotic states involve a notion of
infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a
generalization of scattering amplitudes which depends on twice as many
Grassmann variables. We conjecture that it restores at least half of the
superconformal symmetries, and all of the dual superconformal symmetries. The
object arises naturally as the dual of a null polygonal Wilson loop in an
$(x,\theta,\bar\theta)$ superspace. We support the conjecture by using it to
obtain the total differential of all $n$-point two-loop MHV amplitudes, and
showing that the result passes consistency checks. Potential all-loop
constraints are also discussed.
