Vacuum transitions in two-dimensions and their holographic interpretation

Abstract

We calculate amplitudes for 2D vacuum transitions by means of the Euclidean methods of Coleman-De Luccia (CDL) and Brown-Teitelboim (BT), as well as the Hamiltonian formalism of Fischler, Morgan and Polchinski (FMP). The resulting similarities and differences in between the three approaches are compared with their respective 4D realisations. For CDL, the total bounce can be expressed as the product of relative entropies, whereas, for the case of BT and FMP, the transition rate can be written as the difference of two generalised entropies. By means of holographic arguments, we show that the Euclidean methods, as well as the Lorentzian cases without non-extremal black holes, provide examples of an AdS2/CFT1 ⊂ AdS3/CFT2 correspondence. Such embedding is not possible in the presence of islands for which the setup corresponds to AdS2/CFT1 ⊄ AdS3/CFT2. We find that whenever an island is present, up-tunnelling is possible.

Beyond AdS2/dCFT1: insertions in two Wilson loops

“…Beyond our technical progress in the treatment of Wilson-Maldacena loops in the AdS/CFT correspondence, there is a potential connection that would be interesting to explore further. As noted in the introduction, there is a striking similarity between the Gross-Ooguri phase transition of our set up and the transition in the Page curve for certain models of two-dimensional gravity [26,57]. Given the current interest and insights obtained from gravity in AdS 2 in the form of the Jackiw-Teitelboim model (see reviews [58,59]), it is relevant to precisely clarify which parts of the techniques displayed here can be applied.…”

Vacuum decay actions from tunneling potentials for general spacetime dimension

“…The purpose of this paper is to derive the tunneling action for general d including gravity and to discuss some results. The generalization is straightforward as there are no qualitative changes in behavior but rather a quantitative dependence on d. We restrict the discussion to d > 2 as the d = 2 case requires special modifications (in order to be nontrivial) and deserves a separate study (see [9] and references therein for a recent discussion of vacuum transitions in d = 2). We also leave aside spacetimes with compactified dimensions, in which new instabilities like bubbles of nothing [10] can trigger spacetime decay.…”