The AdS/CFT correspondence establishes a duality between a gravitational theory in an Anti-de Sitter (AdS) spacetime and a conformal quantum field theory on the boundary of the spacetime. This has led to the notion that the spacetime is an emergent concept, but how it emerges from quantum theory on a boundary is not fully understood. In this talk, I will discuss some work in this direction using the theory of von Neumann algebras. Specifically, I will consider a (non-local) conformal Generalized Free Field theory dual to a local scalar field theory in AdS_2 spacetime and will explore the properties of the modular flow and modular conjugation of "time-interval algebras". I will show that these algebras satisfy "Holographic Algebraic Properties". Moreover, I will prove the converse statement that the existence of Holographic Algebraic Properties in any quantum system implies a local QFT in an AdS_2 spacetime. This explains the emergence of a local spacetime in a simple setup.
von Neumann Algebras in Holography and Emergence of Spacetime
von Neumann Algebras in Holography and Emergence of Spacetime