Local Supersymmetry in One-Loop Quantum Cosmology

TL;DR

This paper evaluates the one-loop quantum corrections in Euclidean supergravity with a focus on physical degrees of freedom and boundary conditions, revealing consistent results for the trace anomaly using different methods.

Contribution

It introduces a method to evaluate physical degrees of freedom in one-loop supergravity on bounded Euclidean backgrounds, demonstrating consistency between PDF and spectral boundary conditions.

Findings

Physical degrees of freedom are identified via supersymmetry constraints.

The trace anomaly results are consistent across different boundary conditions.

The PDF method yields results matching spectral boundary condition calculations.

Abstract

The contribution of physical degrees of freedom to the one-loop amplitudes of Euclidean supergravity is here evaluated in the case of flat Euclidean backgrounds bounded by a three-sphere, recently considered in perturbative quantum cosmology. The physical degrees of freedom (denoted by PDF) are picked out by imposing the supersymmetry constraints and choosing a gauge condition. Remarkably, for the massless gravitino field the PDF method and local boundary conditions lead to a result for the trace anomaly which is equal to the PDF value one obtains using spectral boundary conditions on a 3-sphere.