Cohomological Yang-Mills theory in eight dimensions

We construct nearly topological Yang-Mills theories on eight dimensional manifold with a special holonomy group. These manifolds are the Joyce manifold with Spin(7) holonomy and the Calabi-Yau manifold with SU(4) holonomy. An invariant closed four form Tμνρσ on the manifold allows us to define an analogue of the instanton equation, which serves as a topological gauge fixing condition in BRST formalism. The model on the Joyce manifold is related to the eight dimensional supersymmetric Yang-Mills theory. Topological dimensional reduction to four dimensions gives non-abelian Seiberg-Witten equation. (Author). 15 refs., 1 tab