The action of HRT-areas as operators in semiclassical gravity

TL;DR

This paper investigates how HRT-area operators act as transformations on the phase space in semiclassical gravity, revealing their role in shifting entanglement wedges and clarifying their behavior in AdS spacetimes.

Contribution

It provides a rigorous analysis of HRT-area operators' action in Einstein-Hilbert gravity with AdS boundary conditions, connecting geometric transformations to entanglement wedge dynamics.

Findings

HRT-area operators generate specific transformations on the phase space.

The transformations correspond to boosting entanglement wedges.

The results match direct commutator computations in 2+1D Einstein-Hilbert gravity.

Abstract

We study the action of Hubeny-Rangamani-Takayanagi (HRT) area operators on the covariant phase space of classical solutions. It has been previously proposed that this action generates a transformation which, roughly speaking, boosts the entanglement wedge on one side of the HRT surface relative to the entanglement wedge on the other side. We give a sharp argument for a precise result of this form in a general theory of Einstein-Hilbert gravity minimally coupled to matter, taking appropriate care with asymptotically Anti-de Sitter (AdS) boundary conditions. The result agrees with direct computations of commutators involving HRT areas in pure 2+1 dimensional Einstein-Hilbert gravity on spacetimes asymptotic to planar AdS. We also clarify the sense in which this transformation is singular in the deep UV when the HRT-surface is anchored to an asymptotically AdS boundary.