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

Abstract

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.

29+1 pages, some typos fixed

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• Self-Dual Supergravity and Twistor Theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
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• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
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