Einstein gravity from the $\mathbb{N}=4$ spinning particle

We obtain a manifestly background independent BRST quantization of the $\mathbb{N}=4$ supersymmetric spinning particle. We show that nilpotency of the BRST charge $Q$ implies the Einstein equations admitting a cosmological constant of indefinite sign. The physical graviton states are given by the vertex operator, obtained by an infinitesimal variation of $Q$, acting on diffeomorphism ghost states. In addition, the tree-point graviton scattering vertex is correctly reproduced by the worldline computation with these vertex operators.