I will discuss recent advances on the corner proposal, which leverages corner symmetries and their associated algebras in the study of quantum gravity, and demonstrate how the familiar area law for entropy arises in the classical limit. After briefly recalling the notion of corner charges and their algebras in gravitational systems with finite boundaries, I will focus on the two-dimensional case and emphasize its relevance to spherically symmetric four-dimensional spacetimes. Within this framework, I will present the unitary representations of the corner symmetry group, illustrate how entangling surfaces can be described using these states, and explain how to compute the entanglement entropy of subregions. I will then introduce corner coherent states and, through their correspondence with coadjoint orbits, describe the semiclassical limit of the entanglement entropy. Finally, I will connect these results to specific spherically symmetric solutions of Einstein–Hilbert gravity, where the leading term in the semiclassical expansion reproduces the expected Bekenstein–Hawking entropy of the subregion.
From Quantum Corner Symmetries to the Area Law
Host: A.W. Peet