Algebra of operators in an AdS-Rindler wedge

We discuss the algebra of operators in AdS-Rindler wedge, particularly in AdS(5)/CFT4. We explicitly construct the algebra at N = & INFIN; limit and discuss its Type III1 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 & INFIN;. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.

Automated summary

This article discusses the algebra of operators in the AdS-Rindler wedge, particularly in AdS(5)/CFT4. The algebra at the N = ∞ limit is explicitly constructed and its Type III1 nature is examined. The theory's 1/N corrections are considered, and a novel method of renormalizing the Ryu-Takayanagi surface area is utilized to renormalize several divergences, resulting in the algebra becoming Type II∞. This allows for the association of a density matrix with any state in the Hilbert space, leading to a von Neumann entropy.