World volume Supermembrane Instantons in the light-cone frame

In this review we present the octonionic duality for membranes. We start with a discussion on the relation of the Yang Mills theories and the supermembrane Hamiltonian in the light-cone gauge. We further derive the self-duality equations for the membranes and discuss the integrability of the system in 7 and 3 dimensions. Finally, we present classical Euclidean time solutions of these equations and examine the supersymmetries left intact by the self-duality equations.