Higherdimensional analogues of DonaldsonWitten theory
Abstract
We present a DonaldsonWittentype 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 CalabiYau threefolds and manifolds of G_{2} holonomy, respectively. We point out that these theories arise by considering supersymmetric YangMills 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 higherdimensional analogue of the fact that DonaldsonWitten field theory on hyperKähler 4manifolds is topological without twisting. Higherdimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)005154
 arXiv:
 arXiv:hepth/9705138
 Bibcode:
 1997NuPhB.503..657A
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 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