  As open N=2 or 4 strings describe self-dual N=4 super Yang-Mills in 2+2
dimensions, the corresponding closed (heterotic) strings describe self-dual
ungauged (gauged) N=8 supergravity. These theories are conveniently formulated
in a chiral superspace with general supercoordinate and local OSp(8|2) gauge
invariances. The super-light-cone and covariant-component actions are analyzed.
Because only half the Lorentz group is gauged, the gravity field equation is
just the vanishing of the torsion.
