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/1963/216801557nas a2200121 4500008004300000245011100043210006900154520110800223100002101331700002301352700002401375856003601399 2005 en_Ud 00aTopological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry0 aTopological vector symmetry topological gauge fixing of BRSTQFT 3 aThe scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. PoincarĂ© supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds.1 aBaulieu, Laurent1 aBossard, Guillaume1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/1741