@article {2006,
title = {Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds},
journal = {J. Geom. Phys. 56 (2006) 2379-2401},
number = {arXiv.org;hep-th/0412014v2},
year = {2006},
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.},
doi = {10.1016/j.geomphys.2005.12.006},
url = {http://hdl.handle.net/1963/2168},
author = {Laurent Baulieu and Alessandro Tanzini}
}
@article {2005,
title = {Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry},
number = {SISSA;24/2005/FM},
year = {2005},
abstract = {The 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. Poincar{\'e} 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.},
doi = {10.1088/1126-6708/2005/08/037},
url = {http://hdl.handle.net/1963/1741},
author = {Laurent Baulieu and Guillaume Bossard and Alessandro Tanzini}
}