1997/05/31 by B. S. Acharya, Martin O’Loughlin, M. O'Loughlin +2 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cohomology #Combinatorics #Field (mathematics) #Geometric and Algebraic Topology #Geometry #Holonomy #Homotopy and Cohomology in Algebraic Topology #Hyperkähler manifold #Mathematical physics #Mathematics #Pure mathematics #Ricci-flat manifold #String theory #Topology (electrical circuits) #dg-ga #hep-th #math.DG
paper · pdf · doi:10.1016/s0550-3213(97)00515-4
published as Nucl.Phys. B503 (1997) 657-674 · 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
arxiv created 1997/06/04 · openalex publication_date 1997/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.