Axial Gauge in Euclidean Quantum Gravity

TL;DR

This paper applies the axial gauge to Euclidean quantum gravity on manifolds with boundary, deriving boundary conditions that simplify the analysis and show the one-loop divergence matches known transverse-traceless perturbation results.

Contribution

It introduces a boundary-invariant set of conditions using axial gauge in Euclidean quantum gravity, simplifying the calculation of one-loop divergences.

Findings

Boundary conditions enforce vanishing metric perturbations at the boundary.

All ghost modes are eliminated under axial gauge boundary conditions.

One-loop divergence matches three-dimensional transverse-traceless perturbation results.

Abstract

The axial gauge is applied to the analysis of Euclidean quantum gravity on manifolds with boundary. A set of boundary conditions which are completely invariant under infinitesimal diffeomorphisms require that spatial components of metric perturbations should vanish at the boundary, jointly with all components of the ghost one-form and of the gauge-averaging functional. If the latter is taken to be of the axial type, all components of metric perturbations obey Dirichlet conditions, and all ghost modes are forced to vanish identically. The one-loop divergence coincides with the contribution resulting from three-dimensional transverse-traceless perturbations.