On the six-dimensional origin of the AGT correspondence

We argue that the six-dimensional (2, 0) superconformal theory defined on M × C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R4, possibly in the presence of a codimension-two defect operator supported on R2 × C ⊂ M × C. We expect this structure to survive the Ω-deformation.