We consider two dimensional CFT states that are produced by a gravitational path integral.
As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.
As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.
J. Hartle and S. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960.
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
D.N. Page, Density Matrix of the Universe, Phys. Rev. D 34 (1986) 2267 [INSPIRE].
S. Ghoshal and A.B. Zamolodchikov, Boundary S matrix and boundary state in two-dimensional integrable quantum field theory, Int. J. Mod. Phys. A 9 (1994) 3841 [Erratum ibid. 9 (1994) 4353] [hep-th/9306002] [INSPIRE].
S.R. Coleman, Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S.B. Giddings and A. Strominger, Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.16091
About this article
Cite this article
Chen, Y., Gorbenko, V. & Maldacena, J. Bra-ket wormholes in gravitationally prepared states. J. High Energ. Phys. 2021, 9 (2021). https://doi.org/10.1007/JHEP02(2021)009
- 2D Gravity
- Models of Quantum Gravity