The topological B-model on fattened complex and subsectors of N=4 self-dual Yang-Mills theory -: art. no. 042

In this paper, we propose so-called fattened complex manifolds as target spaces for the topological B-model. We naturally obtain these manifolds by restricting the structure sheaf of the N = 4 supertwistor space, a process, which can be understood as a fermionic dimensional reduction. Using the twistorial description of these fattened complex manifolds, we construct Penrose-Ward transforms between solutions to the holomorphic Chern-Simons equations on these spaces and bosonic subsectors of solutions to the N = 4 self-dual Yang-Mills equations on C-4 or R-4. Furthermore, we comment on Yau's theorem for these spaces.