Higher-dimensional analogues of Donaldson-Witten theory
Abstract
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 G2 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-Kähler 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.
- Publication:
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Nuclear Physics B
- Pub Date:
- February 1997
- DOI:
- 10.1016/S0550-3213(97)00515-4
- arXiv:
- arXiv:hep-th/9705138
- Bibcode:
- 1997NuPhB.503..657A
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Differential Geometry
- E-Print:
- 23 Pages, Latex. Our statement that these theories are independent of the metric is corrected to the statement that the theories are invariant under deformations that preserve the holonomy structure of the manifold. We also include more details of the construction of a higher dimensional analogue of Floer theory. Three references are added