Batalin--Vilkovisky quantization and supersymmetric twists

TL;DR

This paper demonstrates that topological twists of supersymmetric mechanics with Kähler targets can be described using Batalin--Vilkovisky quantization, proposing a new way to understand the Hilbert space of states via perverse sheaf cohomology.

Contribution

It introduces a novel connection between topological twists, BV quantization, and perverse sheaves, providing a unified framework for various theories.

Findings

Hilbert space of states expressed via perverse sheaf cohomology

Examples include categorified Donaldson--Thomas invariants and Haydys--Witten theory

Establishes a link between topological twists and BV formalism

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.