W-GRAVITY, N=2 STRINGS, AND 2+2 SU-ASTERISK(INFINITY) YANG-MILLS INSTANTONS

It is conjectured that W gravity can be interpreted as the gauge theory of phi diffeomorphisms in the space of dimensionally reduced D=2+2 SU*(infinity) Yang-Mills instantons. These phi diffeomorphisms preserve a volume-three form and are those that furnish the correspondence between the dimensionally reduced Plebanski equation and the KP equation in (1+2) dimensions. A supersymmetric extension furnishes super-W gravity. The super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields N=1, D=4 SDSG complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface, (T*SIGMA)c, required in the formulation of SU*(infinity) complexified Self-Dual Yang-Mills theory, (SDYM); it naturally follows that the recently constructed D=2+2 N=4 SDSYM theory, as the consistent background of the open N=2 superstring, can be embedded into the N=1 SU*(infinity) complexified self-dual-super-Yang-Mills (SDSYM) in D=3+3 dimensions. This is achieved after using a generalization of self-duality for D>4. Finally, the plausible relationship between the geometry of N=2 strings and the moduli of SU*(infinity) complexified SDSYM in 3+3 dimensions is indicated.