Bra-ket wormholes in gravitationally prepared states

TL;DR

This paper investigates gravitationally prepared states in 2D CFTs, revealing that bra-ket wormholes resolve paradoxes and connect to cosmological models, with implications for entropy and state entanglement.

Contribution

It introduces bra-ket wormholes in gravitationally prepared states, providing new insights into their geometry and entropy in both Euclidean and Lorentzian evolutions.

Findings

Bra-ket wormholes resolve geometric paradoxes in 2D CFT states.

Maximum entropy matches de Sitter entropy in certain states.

Divergent temperatures occur in naive wormhole models.

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 $AdS_2$ 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 $dS_2$ 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.