Abstract

I will first highlight the advantages of adopting an algebraic approach to understand the AdS/CFT correspondence, emphasizing how the algebra of local operators of quantum field theory (QFT) encodes information about spacetime regions. This approach proves particularly advantageous for addressing realistic quantum field theories with infinite-dimensional Hilbert spaces. I will rephrase bulk reconstruction and relative entropy conservation in this algebraic framework, and then utilize the framework to show that they are equivalent. Notably, I will explain the inherent error-correcting properties that arise naturally within this framework and elaborate on the dictionary I am developing bridging operator algebra and holography. Furthermore, I will explain how the framework can be expanded to include non-perturbative gravitational corrections; in this context approximate bulk reconstruction incorporating gravitational errors can be understood through the lens of the privacy/correctability correspondence, which I will motivate. Finally, I will underscore the effectiveness of this algebraic approach in understanding entanglement wedges in spacetime.