It is known that there is a duality between Chern-Simons theory on 3-fold $M$ and topological A-model on the cotangent bundle of this manifold, $T^*M$ (see, for example, the original paper by Witten, Chern-Simons Gauge Theory As A String Theory).
In Topological M-theory as Unification of Form Theories of Gravity Vafa and friends proposed a generalization of the aforementioned duality to the following set of theories:
- Topological gauge theory on 4-fold $M$;
- Topological A-model on twistor space of this manifold, $T(M)$;
- Topological M-theory on certain bundle over M.
Moreover, it is stated that there is a deformation of A-model which is equivalent to full Yang-Mills theory.
I couldn't find a mention of any of these equivalences in the literature. Could anybody recommend some?