Eigenstate Thermalization and Disorder Averaging in Gravity.

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 by adding disorder-averaged replica instantons to the path integral, though their origin is unclear. In this Letter, we show how replica instantons and disorder averaging emerge naturally in an effective theory built from typical microscopic states. We relate replica instantons to a moment expansion of simple operators, and find a microcanonical description in terms of wormholes and Euclidean black holes.

Fine Grained Chaos in AdS_{2} Gravity.

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Holographic stripes.

We construct inhomogeneous asymptotically anti-de Sitter black hole solutions corresponding to the spontaneous breaking of translational invariance and the formation of striped order in the boundary field theory. We find that the system undergoes a second-order phase transition in both the fixed density and fixed chemical potential ensembles, for sufficiently large values of the axion coupling. We investigate the phase structure as a function of the temperature, axion coupling, and the stripe width. The bulk solutions have striking geometrical features related to a magnetoelectric effect associated with the existence of a near-horizon topological insulator. At low temperatures, the horizon becomes highly inhomogeneous and tends to pinch off.

Compressible matter at a holographic interface.

We study the interface between a fractional topological insulator and an ordinary insulator, both described using holography. By turning on a chemical potential we induce a finite density of matter localized at the interface. These are gapless surface excitations which are expected to have a fermionic character. We study the thermodynamics of the system, finding a symmetry preserving compressible state at low temperatures, whose excitations exhibit hyperscaling violation. These results are consistent with the expectation of gapless fermionic excitations forming a Fermi surface at finite density.