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

TL;DR

This paper develops a background-independent BRST quantization of the N=4 supersymmetric spinning particle, deriving Einstein's equations with a cosmological constant and reproducing graviton scattering amplitudes from worldline methods.

Contribution

It introduces a novel BRST quantization approach for the N=4 spinning particle that directly leads to Einstein's equations and reproduces graviton scattering amplitudes.

Findings

Derivation of Einstein equations with an indefinite cosmological constant from BRST nilpotency.

Construction of graviton vertex operators via infinitesimal variations of the BRST charge.

Reproduction of tree-level graviton scattering amplitudes using worldline techniques.

Abstract

We obtain a manifestly background independent BRST quantization of the $\N=4$ 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.