Algebra of operators in an AdS-Rindler wedge

We discuss the algebra of operators in AdS-Rinlder wedge, particularly in AdS${}_5$/CFT${}_4$. We explicitly construct the algebra at $N=\mathrm{\infty }$ limit and discuss its Type III${}_1$ nature. We will consider $1\mathrm{/}N$ 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${}_{\mathrm{\infty }}$. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.