Four-dimensional topological Einstein-Maxwell gravity

The complete on-shell action of topological Einstein-Maxwell gravity in four dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N = 2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The local vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.