  The (2,2) world-sheet supersymmetric string theory is discussed from the
viewpoint of string/membrane unification. The effective field theory in the
closed string target space is known to be the 2+2 dimensional (integrable)
theory of self-dual gravity (SDG). A world-volume supersymmetrization of the
Pleba'nski action for SDG naturally implies the maximal N=8 world-volume
supersymmetry, while the maximal supersymmetrization of the dual covariant
K"ahler-Lorentz-Chern-Simons action for SDG implies gauging a self-dual part of
the super-Lorentz symmetry in 2+10 dimensions. The proposed OSp(32|1)
supersymmetric action for the M-brane may be useful for a fundamental
formulation of uncompactified F theory, with the self-duality being playing the
central role both in the world-volume and in the target space of the M-brane.
