Infinite-Dimensional Holography: Bulk Reconstruction, Relative Entropy, and Operator Algebra

Explore a detailed lecture from CALTECH's Dr. Monica Kang at the Isaac Newton Institute focusing on infinite-dimensional holography and its relationship with quantum field theory. Delve into the algebraic approach to understanding the AdS/CFT correspondence, examining how local operator algebra in quantum field theory contains crucial information about spacetime regions. Learn about bulk reconstruction and relative entropy conservation within this algebraic framework, discovering their equivalence and inherent error-correcting properties. Examine the development of a comprehensive dictionary connecting operator algebra and holography, including discussions on non-perturbative gravitational corrections and approximate bulk reconstruction through the privacy/correctability correspondence. Gain insights into the application of algebraic methods for understanding entanglement wedges in spacetime, particularly relevant for realistic quantum field theories with infinite-dimensional Hilbert spaces.