An Observable in Classical Pure AdS3 Gravity: the Twist along a Geodesic

TL;DR

This paper investigates the twist observable along a geodesic in classical pure AdS3 gravity, revealing its properties and potential role as a central element in the algebra associated with entanglement wedges.

Contribution

It introduces the twist along a geodesic as a new observable in AdS3 gravity and analyzes its properties, including its evolution and commutation relations.

Findings

The twist generates a relative shift along the geodesic.

The twist commutes with the geodesic length.

Supports the idea that the twist is a central element in the algebra.

Abstract

In this paper, we consider a little-studied observable in classical pure AdS3 gravity: the twist along a geodesic. The motivation is that the twist only supports on the geodesic so may be a candidate element in the center of the algebra in either entanglement wedge associated to the geodesic. We study the properties of the twist and get the following results. First, we get the system's evolution generated by the twist, which exhibits a relative shift along the geodesic. Second, we show that the twist commutes with the length of the same geodesic, which supports the proposal that the twist is a candidate element in the center.