Deformation quantisation for $(-2)$-shifted symplectic structures

We formulate a notion of $E_{-1}$ quantisation of $(-2)$-shifted Poisson structures on derived algebraic stacks, depending on a flat right connection on the structure sheaf, as solutions of a quantum master equation. We then parametrise $E_{-1}$ quantisations of $(-2)$-shifted symplectic structures by constructing a map to power series in de Rham cohomology. For a large class of examples, we show that these quantisations give rise to classes in Borel--Moore homology which are closely related to Borisov--Joyce invariants.