Correlators of Worldline Proper Length

TL;DR

This paper develops a method to compute correlation functions of worldline proper length using derivatives of the on-shell action, with applications to AdS/CFT and potential extensions to gravity and interferometry.

Contribution

It introduces a novel approach linking on-shell action derivatives to length correlators and applies this to holographic CFTs to extract worldline observables.

Findings

Derived length-length two-point function from path fluctuations

Proposed logarithm of local correlators as a generating function

Connected worldline correlators to AdS/CFT observables

Abstract

A classical observer can measure elapsed proper time along their worldline. When observers are coupled to a system with internal correlations, measurements of elapsed time may inherit these correlations. We show that derivatives of the on-shell action with respect to worldline mass compute correlation functions of worldline proper length at tree level. We study worldlines coupled to a scalar field. We calculate the length-length two-point function and find it arises from correlated path fluctuations. As an application, we propose that the logarithm of local correlators serves as a generating function of length correlators, which generalizes the on-shell action prescription. Using this proposal, we extract AdS worldline observables from local CFT correlators as computed by Witten diagrams. We briefly discuss extensions to gravity, interferometers, and the holographic encoding of observer time.