Eternal traversable wormhole (1804.00491v3)

Abstract: We construct a nearly-$AdS_2$ solution describing an eternal traversable wormhole. The solution contains negative null energy generated by quantum fields under the influence of an external coupling between the two boundaries. In parallel, we discuss two SYK systems coupled by a relevant interaction. The physics of the two cases is very similar. They both share a "gravitational" subsector which is identical. The solution within this subsector sets the stage for dynamics which is almost conformal invariant. We study this system in detail, both in gravity and in the SYK model. The coupled SYK models have an interesting phase diagram at finite temperature, displaying the usual Hawking-Page transition between the thermal AdS phase at low temperature and the black hole phase at high temperature. Interestingly, these two phases are continuously connected in the microcannonical ensemble.

• The paper demonstrates that engineered boundary interactions in nearly-AdS₂ gravity and coupled SYK models can create stable, eternal traversable wormholes.
• It employs a boundary effective action and negative energy injection to induce traversability, highlighting the role of the Schwarzian mode in low-energy dynamics.
• Results reveal a Hawking-Page-like phase transition that connects quantum gravity insights with chaotic behavior in complex quantum systems.

Detailed Analysis of Eternal Traversable Wormholes and Coupled SYK Models

The paper authored by Juan Maldacena and Xiao-Liang Qi explores the construction and paper of eternal traversable wormholes within the framework of nearly-$AdS_2$ gravity. Simultaneously, it explores analogous phenomena in two coupled Sachdev-Ye-Kitaev (SYK) models. Both settings, despite differing in their foundational constructs, exhibit similar fundamental physics characterized by a shared "gravitational" subsector, central to understanding near-conformal dynamics.

Nearly-$AdS_2$ Gravity and Traversable Wormholes

In nearly-$AdS_2$ gravity, the authors build upon the Jackiw-Teitelboim model, augmented with an external coupling that allows negative null energy flow, contributing to the formation of a traversable wormhole. This interaction is a theoretical leap beyond classical wormholes, which typically require non-trivial topology or exotic matter violating the Averaged Null Energy Condition (ANEC). Instead, the induced negative energy within this model arises from quantum field effects orchestrated by boundary interactions, effectively creating a time-independent and stable traversable wormhole persistent across spacetime.

Analytical Details and Effective Actions

To comprehend the mechanics of these wormholes, the work examines gravity supplemented by boundary interactions translating into an effective action. The profound implication here is the manifestation of a traversable wormhole geometry in an otherwise static AdS space whose dynamics are governed by the Schwarzian action. Often described as emergent from a deeper gauge redundancy, this boundary perspective imbues the wormhole with traversability under subtly engineered conditions — an insight aligned with the holographic principles of AdS/CFT correspondence.

Two Coupled SYK Models

In parallel, the authors consider two coupled SYK models, illustrating a non-gravitational analogue to their gravitational findings. Renowned for its chaotic dynamics and relevance to holography, the SYK model in its decoupled state approximates an $AdS_2$ black hole. Upon introducing an inter-system bilinear coupling, the model's original ground state undergoes significant restructuring, evolving towards a gapped phase. The described interaction configures a wormhole-like structure similar to the traversable wormholes seen in gravity — allowing signal transfer from one side to the other within the SYK pair, thus creating a metaphorical 'wormhole.'

Quantum Effects and Low-Energy Excitations

For low-energy perturbations in these systems, Maldacena and Qi examine the impact of broken reparametrization symmetry. The nearly-conformal region at low energies in the SYK model is governed by the Schwarzian mode, reminiscent of the gravitational analogue. Their analysis unfolds to reveal an energy gap born from the strongly coupled dynamics, reflective of both temporal and geometrical properties intrinsic to the wormhole picture. Intriguingly, this energy gap is precisely controlled by interaction strength, showcasing a tangible consequence of connectivity on the system’s spectral properties.

Thermodynamic Phases and Phase Transitions

The dual examination within gravity and coupled SYK systems dives into their thermodynamics. At low temperatures, the system traverses a stable wormhole phase, whereas at higher temperatures, the configuration transitions into separate black hole states, evidenced by a Hawking-Page-like phase transition. Numerical simulations substantiate these theoretical claims, emphasizing the shared physical mechanisms between the low-energy gravity description and the coupled SYK model’s behavior.

Conclusion and Future Directions

The paper of eternal traversable wormholes in nearly-$AdS_2$ gravity and its horizons within coupled SYK models marks significant progress in understanding connectivity in quantum gravity theories and complex quantum systems. As speculated by the authors, future exploration could unveil similar phenomena across higher-dimensional theories and uncover experimental realizations of SYK-like models in quantum material systems. Advances in such realms may illuminate new forms of quantum matter, further bridging the interplay between quantum information, spacetime geometry, and emergent gravitational phenomena — an avenue promising profound implications for theoretical physics and quantum gravity.