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.

12 pages. Several comments are made to emphasis the novel method performed to renormalize the area of Ryu-Takayanagi surface. Some references added. Corresponds to the published version on JHEP

References in corpus (5)

• Holographic representation of local bulk operators
• An Algebra of Observables for de Sitter Space
• Gravity and the Crossed Product
• On the renormalized volume of hyperbolic 3-manifolds
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories

Cited by in corpus (4)

• Generalized entropy for general subregions in quantum gravity
• Crossed product algebras and generalized entropy for subregions
• A Type $I$ Approximation of the Crossed Product
• On the Nonequilibrium Dynamics of Gravitational Algebras