  We present several expected properties of the holomorphic Floer theory of a
holomorphic symplectic manifold. In particular, we propose a conjecture
relating holomorphic Floer theory of Hitchin integrable systems and
Donaldson-Thomas invariants of non-compact Calabi-Yau 3-folds. More generally,
we conjecture that the BPS spectrum of a $\mathcal{N}=2$ 4-dimensional quantum
field theory can be recovered from the holomorphic Floer theory of the
corresponding Seiberg-Witten integrable system.
