On coefficients of operator product expansions for quantum field theories with ordinary, holomorphic, and topological spacetime dimensions

In many quantum field theories (such as higher-dimensional holomorphic field theories or raviolo theories), operator product expansions of local operators can have as coefficients not only ordinary functions but also 'derived' functions with nonzero ghost number, which are certain elements of sheaf cohomology. We analyse the 'derived' functions that should appear in operator product expansions for a quantum field theory with an arbitrary number of topological, holomorphic and/or ordinary spacetime dimensions and identify necessary and sufficient conditions for such 'derived' functions to appear. In particular, theories with one topological spacetime dimension and multiple ordinary spacetime dimensions provide a smooth analogue of the (holomorphic) raviolo.