Dark Energy and the Spinning Superparticle

TL;DR

This paper explores the BRST algebra of a spinning particle with $ =4$ supersymmetry, revealing connections between background fields, Einstein equations, and the emergence of Einstein metrics from linear excitations.

Contribution

It demonstrates how the BRST algebra constrains background fields to satisfy Einstein equations and shows how certain linear excitations can extend to Einstein metrics.

Findings

BRST algebra implies vacuum Einstein equations with an undetermined cosmological constant.

Cohomology in vacuum background includes free scalar and vector fields.

Certain linear excitations involving vectors can extend to Einstein metrics.

Abstract

We revisit the theory of background fields constructed on the BRST-algebra of a spinning particle with $\mathcal{N}=4$ worldline supersymmetry, whose spectrum contains the graviton but no other fields. On a generic background, the closure of the BRST algebra implies the vacuum Einstein equations with a cosmological constant that is undetermined. On the other hand, in the "vacuum" background with no metric, the cohomology is given by a collection of free scalar- and vector fields. Only certain combinations of linear excitations, necessarily involving a vector field, can be extended beyond the linear level with the vector field inducing an Einstein metric.