  We extend the recently discovered duality between MHV amplitudes and the
light-cone limit of correlation functions of a particular type of local scalar
operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider
the natural generalization of the bosonic correlators to super-correlators of
stress-tensor multiplets and show, in a number of examples, that their
light-cone limit exactly reproduces the square of the matching
super-amplitudes. Our correlators are computed at Born level. If all of their
points form a light-like polygon, the correlator is dual to the tree-level
amplitude. If a subset of points are not on the polygon but are integrated
over, they become Lagrangian insertions generating the loop corrections to the
correlator. In this case the duality with amplitudes holds at the level of the
integrand. We build up the superspace formalism needed to formulate the duality
and present the explicit example of the n-point NMHV tree amplitude as the dual
of the lowest nilpotent level in the correlator.
