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

Abstract

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.

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• A Monte Carlo Approach to the Worldline Formalism in Curved Space
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space