Higher Dimensional Analogues of Donaldson-Witten Theory

Details Higher Dimensional Analogues of Donaldson-Witten Theory Higher Dimensional Analogues of Donaldson-Witten Theory

1997-05-19

arxiv.org/abs/hep-th/9705138v2

Nucl.Phys. B503 (1997) 657-674

Physics

High Energy Physics

High Energy Physics - Theory

23 Pages, Latex. Our statement that these theories are independent of the metric is corrected to the statement that the theori

Scientific paper

10.1016/S0550-3213(97)00515-4

We present a Donaldson-Witten type field theory in eight dimensions on manifolds with $Spin(7)$ holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of $G_2$ holonomy respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher dimensional analogue of the fact that Donaldson-Witten field theory on hyper-K\"ahler 4-manifolds is topological without twisting. Higher dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory.

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