The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory

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.