In 1996 Rozansky and Witten announced a new construction of finite-type invariants of three-manifolds. The invariant comes from the partition function of a topological sigma model, and hence is written as a path integral involving the space of maps from the three-manifold to a hyperkaehler manifold.

In this talk I will discuss the associated 3-dimensional topological quantum field theory. This is joint work with Justin Roberts and Simon Willerton.