Real observers solving imaginary problems

TL;DR

This paper investigates the sphere partition function in Euclidean gravity, revealing how including an observer clarifies the interpretation of the one-loop correction and resolves apparent phase ambiguities.

Contribution

It introduces the role of an observer in Euclidean gravity computations, clarifying the interpretation of the sphere partition function and addressing phase issues in one-loop corrections.

Findings

The phase factor $i^{D+2}$ is mostly canceled when including an observer.

An overall minus sign persists in the corrected interpretation.

Observer inclusion improves understanding of state counting in gravity.

Abstract

The sphere partition function is one of the simplest euclidean gravity computations. It is usually interpreted as count of states. However, the one loop gravity correction contains a dimension dependent phase factor, $i^{D+2}$, which seems confusing for such an interpretation. We show that, after including an observer, this phase gets mostly cancelled for the quantity that should correspond to a count of states. However, an overall minus sign remains.