Batalin--Vilkovisky quantization and supersymmetric twists
Mathematical Physics
2023-08-02 v1 Algebraic Geometry
math.MP
Symplectic Geometry
Abstract
We show that a family of topological twists of a supersymmetric mechanics with a K\"ahler 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.
Cite
@article{arxiv.2107.07218,
title = {Batalin--Vilkovisky quantization and supersymmetric twists},
author = {Pavel Safronov and Brian R. Williams},
journal= {arXiv preprint arXiv:2107.07218},
year = {2023}
}