Worldlines as Wilson Lines

TL;DR

This paper explores the conditions under which non-local gravitational observables, represented as sums over worldlines, can be approximated as quasi-local operators similar to Wilson lines, with a focus on different spacetime geometries.

Contribution

It introduces a framework for understanding when gravitational worldline sums serve as quasi-local operators, highlighting differences across flat, AdS, and de Sitter spaces.

Findings

Operators are quasi-local in flat space and AdS.

Operators fail to be quasi-local in de Sitter space.

Non-local corrections become significant under certain conditions.

Abstract

Gravitational theories do not admit gauge invariant local operators. We study the limits under which there exists a quasi-local description for a class of non-local gravitational observables where a sum over worldlines plays the role of the Wilson line for gauge theory observables. We study non-local corrections to the local description and circumstances where these corrections become large. We find that these operators are quasi-local in flat space and AdS, but fail to be quasi-local in de Sitter space.