Ghost Equations and Diffeomorphism Invariant Theories

TL;DR

This paper reveals that four-dimensional Einstein gravity in the Palatini formalism exhibits a vector supersymmetry linked to the ghost field equations, highlighting a novel symmetry structure in diffeomorphism-invariant theories.

Contribution

It demonstrates the existence of vector supersymmetry in Einstein gravity and connects it directly to the ghost field equations, a novel insight in gravitational gauge theories.

Findings

Vector supersymmetry exists in 4D Einstein gravity.

Supersymmetry is linked to the ghost field equations.

Gravity shares symmetry features with topological Yang-Mills theories.

Abstract

Four-dimensional Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the same type as found in the topological theories for Yang-Mills fields. A peculiar feature of the gravitational theory, characterized by diffeomorphism invariance, is a direct link of vector supersymmetry with the field equation of motion for the Faddeev-Popov ghost of diffeomorphisms.