Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds

Abstract

We 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.

v2: NEW results added in the last Section on the relation with holomorphic Chern Simons and with the topological M theory. References added. PAR-LPTHE P04-32, SISSA-94/2004/FM, 30 pages, LaTeX file

References in corpus (4)

• Black Hole Attractors and the Topological String
• N=2 strings and the twistorial Calabi-Yau
• Topological M-theory as Unification of Form Theories of Gravity
• Complex Counterpart of Chern-Simons-Witten Theory and Holomorphic Linking

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• Conifold geometries, topological strings and multi-matrix models
• Holomorphic field theories and Calabi--Yau algebras
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Reconstruction of N=1 supersymmetry from topological symmetry
• Computing Amplitudes in topological M-theory
• On the Mini-Superambitwistor Space and N=8 Super Yang-Mills Theory
• One-dimensional structures behind twisted and untwisted superYang-Mills theory
• Twisted N=1, d=4 supergravity and its symmetries
• Abelian Varieties, RCFTs, Attractors, and Hitchin Functional in Two Dimensions
• On topological M-theory