Theory HEP Seminar

The Holographic Shape of Entanglement and Einstein's equations

Onkar Parrikar

UPenn

We will study the shape-dependence of entanglement entropy for arbitrary subregions and states in holographic conformal field theories. It is typically hard to work with general states/subregions without relying on symmetries, but we will combine field-theory and gravitational techniques to make progress. Our analysis, when applied to the special case of the vacuum state, will lead to a new perturbative proof (i.e., without using the replica trick) of the Ryu-Takayanagi formula (more precisely, the JLMS formula) for arbitrary subregions. Finally, we will use our results to argue that a general asymptotically AdS spacetime which satisfies the Ryu-Takayanagi formula must necessarily satisfy the non-linear Einstein's equations. Along the way, we will also review earlier progress in understanding the connections between holographic entanglement entropy and Einstein's equations.