Algebra of operators in an AdS-Rindler wedge

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.