From the Corner Proposal to the Area Law

TL;DR

This paper explicitly realizes the Corner Proposal in quantum gravity for spherically symmetric spacetimes, deriving the area law for entanglement entropy through coherent states and classical corner charges.

Contribution

It provides a concrete realization of the Corner Proposal in quantum gravity, connecting corner charges to entanglement entropy and deriving the area law in a specific setting.

Findings

Entanglement entropy proportional to area in semiclassical limit

Explicit construction of quantum corner states and charges

Recovery of Bekenstein-Hawking area law

Abstract

We provide an explicit realization of the Corner Proposal for Quantum Gravity in the case of spherically symmetric spacetimes in four dimensions, or equivalently, two-dimensional dilaton gravity. We construct coherent states of the Quantum Corner Symmetry group and compute the entanglement entropy relative to these states. We derive the classical corner charges and relate them to operator expectation values in coherent states. For a subset of coherent states that we call classical states, we find that the entanglement entropy exhibits a leading term proportional to the area, recovering the Bekenstein-Hawking area law in the semiclassical limit.