Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with vector spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a "hyperkähler weight system".
SAWON, JUSTIN (2001) "Topological quantum field theory and hyperkähler geometry," Turkish Journal of Mathematics: Vol. 25: No. 1, Article 11. Available at: https://journals.tubitak.gov.tr/math/vol25/iss1/11