Faddeev-Popov ghosts in quantum gravity beyond perturbation theory

TL;DR

This paper investigates the non-perturbative ghost sector in asymptotically safe quantum gravity, revealing complex ghost interactions at the ultraviolet fixed point that challenge the traditional Faddeev-Popov structure.

Contribution

It demonstrates the existence of nonzero matter-ghost couplings and higher-order ghost interactions at the non-Gaussian fixed point in quantum gravity.

Findings

Ghost sector includes nonzero matter-ghost couplings.

Higher-order ghost self-interactions are present at the fixed point.

Implications for the RG flow and ultraviolet completion of quantum gravity.

Abstract

We study the Faddeev-Popov ghost sector of asymptotically safe quantum gravity, which becomes non-perturbative in the ultraviolet. We point out that nonzero matter-ghost couplings and higher-order ghost self-interactions exist at a non-Gaussian fixed point for the gravitational couplings, i.e., in the ultraviolet. Thus the ghost sector in this non-perturbative ultraviolet completion does not keep the structure of a simple Faddeev-Popov determinant. We discuss implications of the new ghost couplings for the Renormalization Group flow in gravity, the form of the ultraviolet completion, and the relevant couplings, i.e., free parameters, of the theory.