[Paper Review] Eternal traversable wormhole

Juan Maldacena, Xiao-Liang Qi|arXiv (Cornell University)|Apr 2, 2018

Black Holes and Theoretical PhysicsPhysics and Astronomy41 references227 citations

TL;DR

The authors construct a nearly-AdS2 solution with negative null energy generated by an external boundary coupling, yielding an eternal traversable wormhole, and show a parallel, closely related story in two coupled SYK models with a shared gravitational subsector and similar dynamics.

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.

Motivation & Objective

• Motivate and realize an eternal traversable wormhole by introducing a boundary interaction that yields negative null energy in a nearly AdS2 setup.
• Demonstrate that the gravitational sector and a pair of coupled SYK models share an identical effective description in the low-energy regime.
• Develop and analyze the low-energy effective action (Schwarzian plus boundary interaction) that governs both gravity and SYK dynamics.
• Explore the ground state structure and thermodynamics, including the relation to the thermofield double state and the Hawking-Page-like transition.
• Examine the spectrum and SL(2) symmetry constraints that organize excitations in the coupled system.

Proposed method

• Describe nearly AdS2 gravity with a global time isometry and derive the Schwarzian boundary action.
• Introduce a boundary interaction S_int that couples the two boundaries and generates negative bulk energy.
• Obtain a shared effective action for the gravity and coupled-SYK systems, highlighting the reparametrization (Schwarzian) mode.
• Solve the low-energy theory, including classical solutions and quantization, and relate ground states to the thermofield double.
• Perform large-N and large-q analyses, including numerical studies, to map the phase structure and spectra.
• Translate the gravity results to the SYK language using the two-coupled-SYK framework and match correlators and energy scales.

Experimental results

Research questions

• RQ1 Can a boundary coupling between two sides of nearly AdS2 generate negative null energy enough to render the wormhole traversable?
• RQ2 Do gravity and two coupled SYK models share a common low-energy effective action describing their emergent reparametrization mode?
• RQ3 What is the ground state of the coupled system and how is it related to the thermofield double state of the decoupled system?
• RQ4 What thermodynamic phases arise in the coupled system, and how are they connected across ensembles?
• RQ5 How does the SL(2) structure organize the spectrum of excitations in the coupled system?

Key findings

• A nearly AdS2 solution with two boundaries can be made traversable by introducing an inter-boundary coupling which yields negative null energy.
• The gravity and two coupled SYK systems share an identical low-energy effective action dominated by reparametrization (Schwarzian) dynamics plus a boundary interaction term.
• The ground state of the coupled system is very close to the thermofield double state of the decoupled system at a temperature determined by the coupling strength.
• The coupled system exhibits a phase diagram with a Hawking-Page-type transition between low-temperature (thermal AdS) and high-temperature (black hole) phases, continuously connected in the microcanonical ensemble.
• The spectrum and excitations are governed by an approximate SL(2) symmetry, with the energy scales set by a parameter t′ that controls the gap in the spectrum, as analyzed in large-N and large-q limits.
• The analysis connects gravitational and quantum-mechanical descriptions, providing a unified picture of the traversable wormhole and its SYK realization.