The Ryu-Takayanagi Formula and Extremal Surfaces
This event is part of the HET Seminar Series.
The Ryu-Takayanagi formula and its quantum-corrected version are useful in understanding many aspects of quantum gravity such as subregion duality, emergence of the radial direction, and the generalized second law. In this talk, I will first present a classical argument showing that in the large N limit the von Neumann entropy of a boundary region is given on the extremal surface in the presence of higher derivative corrections, by extremizing the entropy functional among all surfaces homologous to the boundary region. I will then show that all 1/N corrections are systematically obtained by considering the quantum extremal surface, defined by extremizing the generalized entropy which includes the bulk entropy. This is an extension of the Faulkner-Lewkowycz-Maldacena proposal and was conjectured by Engelhardt and Wall. A byproduct of these arguments is a proof of the Ryu-Takayanagi formula without assuming any replica symmetry of the dominant bulk replica solution. I will also introduce the notion of "modular extremal surfaces" and use it to refine subregion duality and bulk reconstruction in AdS/CFT.