Self-dualN=8supergravity as closedN=2(4)strings

As open $N=2\mathrm{} or 4$ strings describe self-dual $N=4\mathrm{}$ Yang-Mills theory in 2+2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) $N=8\mathrm{}$ 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.