The euclidean path integral remains, in spite of its familiar problems, an important approach
to quantum gravity. One of its most striking and obscure features is the appearance of …

In this paper we use the AdS/CFT correspondence to refine and then establish a set of old
conjectures about symmetries in quantum gravity. We first show that any global symmetry …

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum
complexity. I've included (in boldface) various questions that came up during the lecture and …

A bstract We identify conditions for the entanglement entropy as a function of spatial region
to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove …

The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary
region R to the area of an extremal surface in the bulk spacetime. This extremal surface can …

A bstract The reflected entropy SR (A: B) of a density matrix ρ AB is a bipartite correlation
measure lower-bounded by the quantum mutual information I (A: B). In holographic states …

Abstract The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a
holographic theory to the area of a corresponding bulk minimal surface. Using the max flow …

A bstract We consider a black hole in three dimensional AdS space entangled with an
auxiliary radiation system. We model the microstates of the black hole in terms of a field …

Naively, resolving the black hole information paradox requires microscopic details about
quantum gravity. Recent work suggests that, instead, a unitary Page curve can be recovered …

A bstract We present a general procedure for constructing tensor networks that accurately
reproduce holographic states in conformal field theories (CFTs). Given a state in a large-N …