  We propose a 4-dimensional version of topological sigma B-model, governing
maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The
theory depends on on complex structure of X, while is independent of Kaehler
metric of X. The theory is also a 4-dimensiona topological field theory in the
sense that the theory is independent of variation of Riemannian metric of the
source 4-manifold M, potentially leading to new smooth invariant of
4-manifolds. We argue that the theory also comes with a topological family
parametrized by the extended moduli space of complex structures.
