From the Corner Proposal to the Area Law

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.

💡 Research Summary

The paper presents a concrete implementation of the “Corner Proposal” for quantum gravity, focusing on spherically symmetric spacetimes in four dimensions, which are equivalent to two‑dimensional dilaton gravity after dimensional reduction. The central idea of the Corner Proposal is that the algebra of Noether charges associated with diffeomorphisms at a codimension‑2 boundary (the “corner”) – the Extended Corner Symmetry (ECS) algebra – should be quantized first, and its representation theory should serve as the foundation for a quantum theory of gravity, much as the Poincaré algebra underlies particle physics.

In the spherically symmetric case the corner collapses to a single point, and the ECS algebra simplifies to a direct sum of an sl(2,ℝ) sector and two translational generators ℝ². By centrally extending this algebra one obtains the Quantum Corner Symmetry (QCS) group \