Instantons and the monopole-like equations in eight dimensions

We search for an abelian description of the Yang-Mills instantons on certai n eight dimensional manifolds with the special holonomies Spin(7) and SU(4) . By mimicing the Seiberg-Witten theory in four dimensions, we propose a se t of monopole-like equations governing the 8-dimensional U(1) connections a nd spinors, which are supposed to be the dual theory of the nonabelian inst antons. We also give a naive test of the generalized S-duality in the abeli an sector of 8-dimensional Yang-Mills theory. Some problems in this approac h are pointed out.