Mixed Boundary Conditions in Euclidean Quantum Gravity

TL;DR

This paper introduces and analyzes a new class of mixed boundary conditions in Euclidean quantum gravity, examining their effects on trace anomalies and highlighting differences from previously studied boundary conditions.

Contribution

It proposes a novel set of mixed boundary conditions involving Robin conditions on the metric perturbations and evaluates the resulting trace anomaly in flat Euclidean space.

Findings

Trace anomaly differs from previous boundary condition cases

Robin boundary conditions on metric perturbations induce Robin conditions on ghost fields

New boundary conditions lead to distinct anomaly characteristics

Abstract

This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole ghost 1-form. The corresponding trace anomaly is evaluated in the case of flat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly differs from the ones resulting from other local or non-local boundary conditions studied in the recent literature.