Gravitational Algebras in (A)dS2

To construct interesting algebras in quantum gravity, one can dress local field operators to features of the spacetime. I will discuss this first in AdS JT gravity with matter, where matter operators may be dressed to the right or left AdS boundaries. Then, I will consider a scalar field theory in dS2 together with two entangled observers. Each observer carries a clock. As in the AdS example, matter operators may be dressed to either of the two observers. The observers' degrees of freedom are exactly quantized. The algebra of dressed operators teaches us about a putative quantum-mechanical dual theory.