Algebra of operators in an AdS-Rindler wedge

TL;DR

This work analyzes the operator algebra for the AdS-Rindler wedge in AdS$_{5}$/CFT$_{4}$, showing that at large $N$ the subregion algebra is Type III$_{1}$ and can be constructed explicitly via bulk and boundary operators within a thermofield double framework. By renormalizing the infinite horizon volume holographically, a finite center mode $X$ is introduced, upgrading the algebra to Type II$_{\infty}$ and enabling a density matrix formalism. Incorporating $1/N$ corrections then yields a crossed-product algebra that admits trace-class operators and von Neumann entropy for states. The results connect to generalized entropy and offer a concrete renormalization scheme for the Ryu-Takayanagi surface in the AdS-Rindler context, with implications for finite-$N$ behavior and holographic entanglement.

Abstract

We discuss the algebra of operators in AdS-Rinlder wedge, particularly in AdS$_{5}$/CFT$_{4}$. We explicitly construct the algebra at $N=\infty$ limit and discuss its Type III$_{1}$ nature. We will consider $1/N$ corrections to the theory and using a novel way of renormalizing the area of Ryu-Takayanagi surface, describe how several divergences can be renormalized and the algebra becomes Type II$_{\infty}$. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.