General relativity and topological string duality through Penrose-Ward transform

This paper discusses the relation between topological M-theory, self-dual Yang-Mills and general relativity. We construct a topological membrane field action from Witten's cubic string field theory, which reduces to topological Yang-Mills on a one-parameter family of conifolds. It turns out that this can be interpreted as the twistor space of the four-dimensional Lagrangian submanifold M for large momenta. From the viewpoint of the target, we find that A-model and B-model on M unify in the topological membrane theory through the Penrose-Ward transform. The partition function is constructed and it is shown that, in the weak-coupling regime, it is equal to the partition function of Donaldson-Witten theory. Additionally, homological mirror symmetry, background independence as well as role of knot cobordisms as topological two-branes is discussed. It is outlined that all types of Floer homology are part of the topological membrane theory. Additionally, we find evidence that in the non-perturbative regime, the partition function of the membrane field action and that of the partially twisted (2,0) SU(N) superconformal field theory on the worldvolume of N topological fivebranes must coincide.

Automated summary

This paper discusses the relationship between topological M-theory, self-dual Yang-Mills, and general relativity. It introduces a topological membrane field action derived from Witten's cubic string field theory, demonstrates the unification of A-model and B-model on the four-dimensional Lagrangian submanifold M through the Penrose-Ward transform in topological membrane theory, and constructs the partition function which is equivalent to Donaldson-Witten theory in the weak-coupling regime. It also explores topics such as homological mirror symmetry, background independence, and the role of knot cobordisms as topological two-branes. The study suggests that all types of Floer homology are part of the topological membrane theory and provides evidence for the equivalence of the partition functions between the membrane field action and the partially twisted (2,0) SU(N) superconformal field theory on the worldvolume of N topological fivebranes in the non-perturbative regime.