01554nas a2200109   4500008004300000245008800043210006900131520116300200100002101363700002401384856003601408       2006                        en_Ud  00aTopological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds0 aTopological symmetry of forms N1 supersymmetry and Sduality on s3 aWe study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.1 aBaulieu, Laurent1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/2168