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.
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Acknowledgments
We thank Ahmed Almheiri, Sebastián Céspedes, Shanta de Alwis, Alexander Frenkel, Iñaki García Etxebarria, Victor Gorbenko, Steven Gratton, Prem Kumar, Yolanda Lozano, Juan Maldacena, Francesco Muia, Carlos Nuñez, Jorge Santos, Sakura Shäfer-Nameki, Savdeep Sethi, Ronak Soni, Julian Sonner, Mark Van Raamsdonk, Aron Wall and Edward Witten for helpful conversations. We also wish to thank the anonymous referee for helping us in improving the paper. The work of VP is partially supported by an STFC scholarship through DAMTP, and has been partially supported by an Angelo Della Riccia fellowship for the academic year 2020/21. The work of FQ has been partially supported by STFC consolidated grants ST/P000681/1, ST/T000694/1.
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Pasquarella, V., Quevedo, F. Vacuum transitions in two-dimensions and their holographic interpretation. J. High Energ. Phys. 2023, 192 (2023). https://doi.org/10.1007/JHEP05(2023)192
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DOI: https://doi.org/10.1007/JHEP05(2023)192