Description
Given a smooth 4-manifold M4, what algebras act on (generalized) cohomology of instantons on M4? One can tackle this question either directly or take an equivalent route suggested by the (conjectural) existence of super-conformal theory in six dimensions. The latter does not have enough supersymmetry to be defined on an arbitrary 6-manifold, but can be made fully topological on a 4-manifold and holomorphic in the resulting two dimensions. Such topological+holomorphic twist of 6d fivebrane theory leads to a large class of vertex algebras labeled by smooth 4-manifolds, in such a way that different cutting and gluing operations on 4-manifolds lead to their counterparts in VOA[M4] and equivalent ways of constructing 4-manifolds manifest themselves as equivalences of VOAs. This talk is based on the recent and ongoing work with Boris Feigin.
