Instantons and the monopole-like equations in eight dimensions

We search for an abelian description of the Yang-Mills instantons on certaineight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). Bymimicing the Seiberg-Witten theory in four dimensions, we propose a set ofmonopole-like equations governing the 8-dimensional U(1) connections andspinors, which are supposed to be the dual theory of the nonabelian instantons.We also give a naive test of the generalized $S$-duality in the abelian sectorof 8-dimensional Yang-Mills theory. Some problems in this approach are pointedout.Comment: 22+1 pages, no figures, using JHEP.cls; v2: typos corrected and refs updated, to appear in JHE