# Batalin--Vilkovisky quantization and supersymmetric twists

@inproceedings{Safronov2021BatalinVilkoviskyQA, title={Batalin--Vilkovisky quantization and supersymmetric twists}, author={P. Safronov and B. Williams}, year={2021} }

We show that a family of topological twists of a supersymmetric mechanics with a Kähler target exhibits a Batalin–Vilkovisky quantization. Using this observation we make a general proposal for the Hilbert space of states after a topological twist in terms of the cohomology of a certain perverse sheaf. We give several examples of the resulting Hilbert spaces including the categorified Donaldson–Thomas invariants, Haydys–Witten theory and the 3-dimensional A-model.

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