Coarse graining pure states in AdS/CFT

Abstract

We construct new Euclidean wormhole solutions in AdSd+1 and discuss their role in UV-complete theories, without ensemble averaging. The geometries are interpreted as overlaps of GHZ-like entangled states, which arise naturally from coarse graining the density matrix of a pure state in the dual CFT. In several examples, including thin-shell collapsing black holes and pure black holes with an end-of-the-world brane behind the horizon, the coarse-graining map is found explicitly in CFT terms, and used to define a coarse-grained entropy that is equal to one quarter the area of a time-symmetric apparent horizon. Wormholes are used to derive the coarse-graining map and to study statistical properties of the quantum state. This reproduces aspects of the West Coast model of 2D gravity and the large-c ensemble of 3D gravity, including a Page curve, in a higher-dimensional context with generic matter fields.

Cosmology from random entanglement

“…In this notation, X " X AdS|AdS , and X BH|BH corresponds to the Euclidean solution represented in figure 5. The last two, X BH|AdS and X AdS|BH , contain mixed components, and provide initial data of one-sided black hole microstates entangled to AdS regions, similar to those described in [77]. Note that the black hole component X BH only exists above the critical temperature for AdS black hole solutions.…”

“…In JT gravity coupled to matter particles, this class of states were dubbed partially entangled thermal states (PETS) in [72]. More recently, analogous microstates have been considered in a variety of different contexts, including extremal supersymmetric black holes [73,74] and higher dimensional neutral black holes [66,67,75] (see also [76][77][78] for one-sided analogs and B-states).…”

The Virasoro minimal string

“…particularly Euclidean wormhole partition functions, are nontrivially reproduced by statistical averages over 2d CFT data [152,153]. The precise nature of such an ensemble description remains elusive (but see [154] for recent progress), and many Euclidean wormhole partition functions may instead be interpreted in terms of coarse-graining microscopic data of individual CFTs [155][156][157]. The Virasoro minimal string now leads to the concrete prediction that the near-extremal limit as defined in the previous paragraph of the random ensemble of 2d CFTs is governed by the Virasoro matrix integral.…”

Coarse-graining black holes out of equilibrium with boundary observables on time slice

“…In [40], the bulk dual of the one-point entropy was first conjectured to be the causal holographic information [42,43], but unfortunately, counterexamples were identified in [44], leading the authors to conclude that the bulk counterpart seems more intricate than initially proposed. Other approaches, as seen in [45][46][47][48], begin with defining their coarse-graining procedures in the bulk. While [45,47] and [48] employ different ways of coarse-graining, both approaches are associated with the apparent horizon, presenting intriguing implications to gravity and its thermodynamics.…”

“…Other approaches, as seen in [45][46][47][48], begin with defining their coarse-graining procedures in the bulk. While [45,47] and [48] employ different ways of coarse-graining, both approaches are associated with the apparent horizon, presenting intriguing implications to gravity and its thermodynamics. However, as noted by the authors, none of those approaches has yet acquired a complete description within the boundary language.…”