Quantum Information Probes in Holography: Shell Geometries and Black Hole Singularities

Abstract

A remarkable aspect of the AdS/CFT correspondence and related holographic dualities is the way quantities related to quantum information in the non-gravitational boundary theory are geometrized by the bulk gravitational theory. The most well known example is the relationship between minimal surfaces in the bulk and the boundary entanglement entropy, as described by the Ryu-Takayanagi formula. Another example is measures of quantum complexity, whose bulk duals are believed to be a class of geometric bulk observables called ``complexity=anything'' that we explain in the main body of the thesis. In this thesis, we study these holographic quantum information probes in two families of geometries that arise either in AdS/CFT or in related string-theory derived dualities. We explore the two families of geometries for essentially different purposes.

First, we consider so-called shell geometries, which are sourced by a spherical distribution of Dp-branes. We are interested in these geometries as they contain within the shell a region of flat spacetime. Hence, this setup gives us a clean way to study a region of flat spacetime geometry in a setting with a controlled holographic dual theory. Our motivation is then to use this setup to extract lessons relevant for the quest to understand holography in asymptotically flat spacetimes. To this end, we study the holographic entanglement entropy and associated entropic c-functions in these backgrounds. We also explore the properties of so-called internal RT surfaces in these geometries, and draw a connection to RT surfaces in asymptotically flat spacetimes. We also briefly evaluate a holographic complexity observable in this background, and confirm that the result is compatible with the conclusion of the entanglement entropy calculations. We conclude that the creation of the flat space region entails a drastic reduction in effective IR degrees of freedom in the boundary theory.

Then, we investigate how so-called complexity=anything observables encode the interior geometry of (d+1)-dimensional asymptotically AdS black holes. The flexibility of this class of observables allows the corresponding extremal surfaces to be pushed arbitrarily close to the spacelike singularity, and we show that their late-time growth rate carries information about the near-singularity geometry. After resolving a puzzle concerning codimension-one observables near the singularity, we evaluate observables defined on constant-mean-curvature slices and find that the late-time growth rate depends on the value of the mean curvature, which controls how deeply the slices probe the interior. This family of observables then encodes properties of the interior region. Comparing the uncharged and charged cases, we find that for AdS-Reissner–Nordström black holes these observables only probe the interior up to the inner horizon, so in this case the observables do not reveal the presence of a singularity.