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

TL;DR

This paper introduces fattened complex manifolds as target spaces for the topological B-model, establishing a connection with subsectors of N=4 self-dual Yang-Mills theory through twistorial methods.

Contribution

It defines fattened complex manifolds via fermionic reduction of supertwistor space and constructs Penrose-Ward transforms linking holomorphic Chern-Simons solutions to Yang-Mills subsectors.

Findings

Fattened complex manifolds serve as new target spaces for the B-model.

Penrose-Ward transforms relate these manifolds to Yang-Mills solutions.

Comments on Yau's theorem for these spaces are included.

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.