Abstract
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.
Highlights
1.1 General motivationRecent work has highlighted the useful properties of the fine grained entropy formula, the Ryu-Takayanagi formula and its generalizations [1,2,3,4], for understanding properties of states in quantum gravity
To summarize the above discussion, we found that the dS2 JT gravity plus matter CFT theory “almost” has classical bra-ket wormhole solutions that bear similarities with the bra-ket wormholes in AdS2 and can resolve the strong subadditivity problem present in the Hartle-Hawking state
We note that the wormhole geometry of our length-π contour appears similar to the “double-trumpet” solution studied in [31] which is responsible for the “ramp” in the time dependence of the spectral form factor in SYK-like theories, see figure 23
Summary
Recent work has highlighted the useful properties of the fine grained entropy formula, the Ryu-Takayanagi formula and its generalizations [1,2,3,4], for understanding properties of states in quantum gravity. This formula is believed to give an accurate estimate for the fine grained entropy of the exact state in terms of a computation that can be done knowing only the semiclassical solution, a background geometry plus propagating quantum fields. While this is an initially pleasing answer, further study revealed that there were inconsistencies with this result
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