Causal connectability between quantum systems and the black hole interior in holographic duality

Abstract

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We address these issues in this paper. In particular, we (i) present a boundary formulation of a class of in-falling bulk observers; (ii) present an argument that a sharp bulk event horizon can only emerge in the infinite N limit of the boundary theory; (iii) give an explicit construction in the boundary theory of an evolution operator for a bulk in-falling observer, making manifest the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A by-product is a concept called causal connectability, which is a criterion for any two quantum systems (which do not need to have a known gravity dual) to have an emergent sharp horizon structure.

Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?

“…In the high termperature phase, the analogy with statistical mechanics suggests that the natural algebra of single trace operators would be of Type III. Indeed, this has been argued recently by Leutheusser and Liu [22], who made this claim partly based on the AdS/CFT duality, in a paper with several novel ideas about quantum black holes. These issues and some subtle corrections to the large N limit will be further discussed elsewhere [23].…”

“…This article was originally planned as an exposition of those matters, along the lines of a lecture at the 2021 Bootstrap Summer School, where the most important points are outlined [21]. However, a recent article by Leutheusser and Liu [22], with some novel observations about quantum black holes, suggested that it would be worth while to discuss from a similar point of view the large N limit of gauge theory. These issues are briefly discussed in section 4.…”

Emergent times in holographic duality

“…We will consider the large ν limit and expand various quantities in (11.1)-(11.2) in 1/ν. 28 To define the limit, we will also scale frequency and spatial momenta as [4] ω = νu, q = νp, k = (u, p) fixed, ν → ∞ . (11.4)…”

“…A summary of the main idea and results has appeared earlier in[28] 2. For reviews on the classification of von Neumann algebras see chapter III.2 of[29] or section 6 of[30].…”

Trans-IR Flows to Black Hole Singularities

“…For example the critical time t c (Section IV B) is a γ-independent quantity found by forcing left-moving and right-moving null rays to meet at Re(t) = 0. One may wonder how the infinitude of choice in γ may correspond to infinite families of observables in the boundary theory [73].…”