Observing quantum gravity in asymptotically AdS space

Abstract

A question is studied whether an observer can discover quantum gravity being in the semi-classical regime. It is shown that it is indeed possible to probe a certain quantum gravity effect by employing an appropriately designed detector. The effect is related to the possibility of having topologically inequivalent geometries at once in the path integral approach. A CFT state which is expected to describe the eternal AdS black hole in the large N limit is discussed. It is argued under certain assumptions that the black hole boundary should be merely a patch of the entire AdS boundary. This leads then to a conclusion that that CFT state is the ordinary CFT vacuum restricted to that patch. If existent, the bulk CFT operators can behave as the ordinary semi- classical quantum field theory in the large N limit in the weak sense.Comment: typos fixed; to be published in Physical Review

Quantum vacuum near non-rotating compact objects

“…It has been recently argued that these states are in tension with the Einstein equivalence principle [3] (for further relevant references, see [4,5] and [6][7][8][9]) 1 . The argument is based on the observation that one can distinguish in these vacua a static gravitational field from a uniformly accelerating frame by performing a local quantum experiment.…”

Holography versus correspondence principle: Eternal Schwarzschild–anti–de Sitter geometry

“…Indeed, the same inverse temperature β characterises two different states, namely the AdS space with the thermal gas and the Hartle-Hawking state restricted to the region outside of the black hole. In the path integral approach in the saddle-point approximation, both phases are coexisting, described by a non-extremal KMS state 11 and can be distinguished by an appropriately designed observable [41].…”

“…During the Hawking-Page transition, the causal propagator of the field ΦM (x) changes as the global structure of space changes. In other words, ∆ M 1 (x, x ′ ) = ∆ M 2 (x, x ′ ) as it can be seen, for example, if one compares anti-symmetric combination of two-point correlation functions in M 1 and M 2 for a scalar field model conformally coupled to gravity [41]. However, the boundary is still compactified Minkowski space and the CFT algebra is still invariant under the conformal algebra so (2,3).…”

Near-horizon physics of an evaporating black hole: One-loop effects in the λΦ^4-theory

“…In general, any polynomial composed of the operator Φ> (x) probes |Ω as an empty state, while composed of Φb (x) as if |Ω is a mixed state. It is worth emphasising that the latter effect is due to the field operator Φb (x), rather than the vacuum state (see for an earlier version of this point [16,17]). 3 It is tempting to conclude that particles | ψ defined as…”

“…close to the horizon, while σ(x, x ′ ) can be found in [17] and approaches in the limit R → r H to the geodetic interval of the static space with the hyperbolic spatial section. Substituting σ(x, x ′ ) into the Hadamard parametrix, we find that…”