Traces and Time: a de Sitter Black Hole correspondence

TL;DR

This paper introduces an algebraic framework linking de Sitter space and black holes through an extra quantum degree of freedom, enabling finite trace definitions and an algebraic interpretation of Page's curve.

Contribution

It proposes a novel algebraic approach that associates de Sitter and black hole horizons with type II_1 factors, incorporating a quantum clock to define finite traces.

Findings

Associates dS and BH with type II_1 factors

Defines a quantum clock to promote the extra degree of freedom

Derives an algebraic version of Page's curve

Abstract

We describe how general covariance for QFT defined on a space-time background with horizons leads to the need of adding an extra quantum degree of freedom. The definition of traces and entropies involves the use of a formally thermal state (weight) on the algebra of observables of the added degree of freedom. This extra degree of freedom is promoted into a physical clock after defining an hermitian and positive clock Hamiltonian. The so modified weight can be used to associate to both dS and the BH a type $II_1$ factor and a finite trace. The Murray-von Neumann dimension ( coupling constant) for this type $II_1$ description of the black hole naturally produces an algebraic version of Page's curve.