This question is about the 6d (2, 0) superconformal field theory (also called 'theory X' by some people). This SCFT, which can be considered as a relative quantum field theory (see here for a definition), exhibits a great deal of mathematical structure which is cogently expressed in the diagram below (taken from slides for D. Ben-Zvi's talk). In particular, its compactification on 2-torus is $N=4$ Yang--Mills theory. Note that the S-duality of the compactification of a topological twist of $N=4$ SYM (the so-called Kapustin--Witten TQFT) on a closed Riemann surface encodes geometric Langlands duality.

My question is: has there been any recent progress on understanding the compactification of theory X on general 4-manifolds (marked as '???' in the diagram)?