Seminarium Teorii Względności i Grawitacji

I will discuss recent advances on the corner proposal, which leverages corner symmetries and their associated algebras to study quantum gravity, and demonstrate how the familiar area law for entropy emerges in the classical limit. After briefly recalling the notion of corner charges and their algebras in gravitational systems with finite distance boundaries, I will focus on the two-dimensional case and present the example of the dimensionally reduced, spherically symmetric Einstein-Hilbert theory in four dimensions. I will then move to the quantum description by introducing the unitary representations of the corner symmetry group, illustrating how entangling surfaces can be described in terms of these states and how to compute the entanglement entropy of subregions. Finally, I will introduce corner coherent states to connect the quantum theory with the classical charges and show that a subset of these states reproduces the area law for Schwarzschild black holes in the semiclassical limit.