Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a
useful point of view on the Donaldson and Seiberg-Witten invariants of
four-manifolds. In this paper we generalize the construction to include a path
integral formulation of generalizations of Donaldson invariants for smooth
families of four-manifolds. Mathematically these are equivariant cohomology
classes for the action of the oriented diffeomorphism group on the space of
metrics on the manifold. In principle these cohomology classes should contain
nontrivial information about the topology of the diffeomorphism group of the
four-manifold. We show that the invariants may be interpreted as the standard
topologically twisted path integral of four-dimensional N=2
supersymmetric Yang-Mills coupled to topologically twisted background fields of
conformal supergravity.Comment: 79 pages + appendices = 166 pages; 1 figure; Hyperlinks fixe