Topological twisting of conformal supercharges

Putting a twisted version of N=4 super-Yang-Mills on a curved four-dimensional manifold generically breaks all conformal supersymmetries. In the special case where the four-manifold is a cone, we show that exactly two conformal supercharges remain unbroken. We construct an off-shell formulation of the theory such that the two unbroken conformal supercharges combine into a family of topological charges parameterized by CP1. The resulting theory is topological in the sense that it is independent of the metric on the three-dimensional base of the cone.