Abstract: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 N = 2 4-dimensional quantum field theory can be recovered from the holomorphic Floer theory of the corresponding Seiberg-Witten integrable system.
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