Bra-ket wormholes in gravitationally prepared states

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.

Overview of "Bra-ket wormholes in gravitationally prepared states"

In "Bra-ket wormholes in gravitationally prepared states," Chen, Gorbenko, and Maldacena explore unconventional states in Conformal Field Theories (CFTs) that are formed through gravitational path integrals in simplified models of quantum gravity. The study focuses on two main configurations: one involving Euclidean AdS$_2$ spaces and the other involving Lorentzian de Sitter (dS) spaces, both leading to a final state in a flat space where gravity is negligible. These setups correspondingly represent holographic duals associated with specific quantum states in a non-gravitational region, prompting the examination of entropic properties, particularly under the gravitational fine-grained entropy formula.

Euclidean AdS$_2$ Configuration

The authors begin with a system where a boundary state in the CFT is formed by Euclidean AdS$_2$ evolution. The naive semiclassical geometry presumes this state is a simple vacuum. However, quantum corrections prompt the consideration of non-trivial islands, potentially resolving the entropic saturation at the value related to the black hole entropy, $2S_0$. Crucially, the authors introduce "bra-ket wormholes," alternative semiclassical geometries joining the bra with the ket contours in the gravitational path integral. These wormholes ensure that entropy is calculated correctly, addressing the subadditivity paradox through a pure, yet thermal-like state when considering the flat space region's entanglement with an expanding and then collapsing closed FLRW universe.

Lorentzian dS$_2$ Configuration

The authors further extend their exploration into a cosmological context by modeling an inflationary phase in dS$_2$ followed by flat space evolution. The naive geometry utilizes the Hartle-Hawking prescription but encounters entropy subadditivity problems analogous to the AdS$_2$ setting. Here, bra-ket wormholes are once again considered, invoking complex contour paths to create an entangled state across the bra and ket boundaries. Several contours are examined, with the most promising leading to a divergent temperature that aligns with traditional Hartle-Hawking expectations in fields like cosmology.

Analytical Implications and Broader Perspective

The introduction of bra-ket wormholes offers insights into resolving entropic inconsistencies that arise in the naive state from gravitational preparations. Their presence underscores how entangled states formed from gravitational evolution can far exceed the simple vacuum interpretations, requiring corrections that consider the interconnected nature of bra and ket states. Notably, the study affirms that such wormholes provide valid entropic results without breaching purity, substantiating their contribution as a genuine resolution to known paradoxes in quantum gravity.

The implications reach further, suggesting a novel approach to understanding closed cosmologies through entanglement with regions where gravity is dormant. This could indicate a profound encoding of cosmological dynamics via boundary states or quantum entanglement—a concept reminiscent of ER=EPR but in a cosmological framework.

Future Outlook

The paper provides substantial groundwork for re-evaluating the quantum states prepared by gravity, hinting at potential advancements in cosmological and holographic theories. The bra-ket wormhole concept introduces a paradigm shift in how entropic properties and state preparations may be analyzed, offering routes to deeper understanding of quantum gravity's subtleties. The notion of resolving subadditivity through such linked spacetime configurations could be pivotal in future research aimed at disentangling the complexities of quantum cosmology and holography. Further investigations could aim to develop these ideas into higher-dimensional models and verify their consistency within more general setups.