Cohomological Yang-Mills Theory in Eight Dimensions

Details Cohomological Yang-Mills Theory in Eight Dimensions Cohomological Yang-Mills Theory in Eight Dimensions

1997-05-17

arxiv.org/abs/hep-th/9705127v1

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, latex, Talk given at APCTP Winter School on Dualities in String Theory, (Sokcho, Korea), February 24-28, 1997

Scientific paper

We construct nearly topological Yang-Mills theories on eight dimensional manifolds 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 $T_{\mu\nu\rho\sigma}$ 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.

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