Now that the question is open again (now in my paraphrasing), maybe I'll repost my reply from the nForum with some brief comments thrown in:

That the 6-dimensional (2,0)-superconformal QFT on the worldvolume of the M5-brane yields N=2 D=4 super Yang-Mills theory under Kaluza-Klein compactification on a 2d Riemann surface was known since about the mid 90s. Edward Witten had famously advertized this in the Proceedings to Graeme Segal's 60th birthday conference that by this construction the remaining invariance under Moebius transformations of that compactification manifold geometrically explains the "Montonen-Olive"/"electric-magnetic" S-duality invariance of (super) Yang-Mills theory.

Later he realized further compactification of this down to 2-dimensions as a geometric realization of geometric Langlands duality. In the course of this the N=2 D=4 super Yang-Mills theory is "topologically twisted" in a way analogous to the well-known twisting of N=4 SYM that goes back to the work that won him the Fields medal. The twisting of the N=2 theory then also showed up in the more recent work by Gaiotto et al. that lead to the AGT correspondence.

While the details for the topological twisting of the N=2 supersymmetric field theory are a tad more involved than those of the N=4 theory, the basic idea is the same: one picks an embedding of the spacetime rotation symmetry into the R-symmetry group (the one under which the supercharges transform) and then asks for a linear combination $Q$ of the supercharges that is held fixed by the resulting external+internal symmetry transformations. The cohomology of this $Q$ is then seen to pick inside the quantum observables of the origional super gauge field theory those of a topological field theory. That is the topologically twisted theory.

Pointers to more details on this topological twisting that the above questing is after are collected here:

http://ncatlab.org/nlab/show/topologically+twisted+D=4+super+Yang-Mills+theory

Pointers specifically concerning the twistied Kaluza-Klein compactification of the M5-brane on a Riemann surface to a topologically twisted N=2 super Yang-Mills theory are here:

http://ncatlab.org/nlab/show/N=D2+D=4+super+Yang-Mills+theory#ReferencesConstructionFrom5Branes

This post imported from StackExchange MathOverflow at 2014-12-24 12:04 (UTC), posted by SE-user Urs Schreiber