Seminarium Teorii Względności i Grawitacji

In my talk, I will begin by introducing the Universal Corner Algebra (UCA), a universal algebra of symmetries associated with corners (the boundaries of regions), within the context of classical General Relativity (GR). I will then argue that the UCA should play a role in Quantum Gravity similar to the role the Poincaré algebra plays in quantum field theory. Moving on to a two-dimensional example, I will explain how the UCA acquires a central extension in quantum theory and explore how the resulting representation theory of Quantum Corner Algebra (QCA) can be used to combine two regions into one. Additionally, I will demonstrate how these representations can be applied to compute the entanglement entropy of two regions and speculate on how this might be used to reconstruct the semiclassical spacetime. Finally, if time permits, I will briefly discuss the structure of QCA in 3 dimensions.