Traversable Wormholes

Definition

A traversable wormhole is a Lorentzian geometry connecting two asymptotic regions through a throat that a causal signal (or observer) can actually cross. Classically this is forbidden: keeping the throat open requires defocusing of null geodesics, i.e. $\int T_{kk}d\lambda <0$ along the crossing ray, which violates the averaged null energy condition (ANEC). Any traversable wormhole therefore needs a quantum source of negative null energy.

The modern, controlled realization is the Gao–Jafferis–Wall (GJW) construction: starting from the two-sided eternal black hole (whose Einstein–Rosen bridge is non-traversable and is dual to the thermofield double), one turns on a double-trace coupling between the two boundaries,

$$\delta S=\int dtg(t){\mathcal{O}}_L(t){\mathcal{O}}_R(t),$$

which produces a one-loop negative average null energy in the bulk and opens the throat just enough for a signal to pass. The coupling makes the two boundaries communicate: it is the bulk dual of a teleportation / Hayden–Preskill protocol.

Two regimes recur:

• One-shot (GJW): a brief coupling opens the wormhole transiently; a signal sent in at the right moment emerges on the other side (regenesis).
• Eternal (Maldacena–Qi): two systems (e.g. two SYK dots) kept permanently coupled have a near-AdS${}_2$ ground state that is a steady-state traversable wormhole — a renewable entangled resource.

Role in Research

Traversable wormholes are the sharpest meeting point between the group’s algebraic-QFT tools and holographic gravity, for three reasons:

1. The GJW coupling is a Connes-cocycle perturbation. $V=g{\mathcal{O}}_L{\mathcal{O}}_R$ perturbs the modular flow of the TFD exactly in the manner the group’s crossed-product and relative-entropy machinery handles (Ahmad–Jefferson make this precise). A free-field two-wedge analogue with $V=gW(f_L)W(f_R)$ is directly computable — see relative-entropy-wormhole-opening.

2. Traversability versus Bell-CHSH. A maximal Bell-CHSH violation between two regions presumes their algebras commute (no signaling). Opening the wormhole introduces signaling across the throat, so there should be a quantitative tension between traversability and achievable violation — see bell-chsh-across-traversable-wormhole.

3. A teleportation resource. Regenesis through the wormhole is a physical channel for moving quantum information, inviting comparison with embezzlement from a type III₁ resource.

This concept anchors Semester II of the algebraic-QFT course (Blocks 4–5: GJW, MSY, AAJ). In the holography course, the Gao–Jafferis–Wall coupling appears in Lecture 23 and Jefferson’s description of it as a modular inclusion in Lecture 30.

Relations

• Built on the thermofield double state and the ER=EPR correspondence.
• Requires ANEC violation; contrast with the non-traversable Einstein–Rosen bridge of the eternal black hole.
• Treated algebraically via the crossed product and Connes cocycle (Ahmad–Jefferson).
• Probed by relative entropy and Bell-CHSH in the group’s programs.
• Part of the gauge-gravity-duality area and the wormholes-and-quantum-information-qft connection.

Papers

• 2021-kundu-wormholes-holography — §5.2 reviews GJW, Maldacena–Qi, braneworld wormholes, and regenesis.
• Gao, Jafferis, Wall (2017), arXiv:1608.05687 — the original double-trace mechanism.
• Maldacena, Qi (2018), arXiv:1804.00491 — eternal traversable wormhole from coupled SYK.
• Maldacena, Stanford, Yang (2017), arXiv:1704.05333 — bulk “diving in” analysis.
• Ahmad, Jefferson (2025), arXiv:2501.01487 — algebraic / cocycle treatment.

Notes

The honest scoping point stressed in the course: the algebra sees the cocycle-perturbed modular data, but the Shapiro time advance and geometric “opening” of the throat are bulk statements the boundary algebra does not directly resolve. Keeping this algebra/bulk demarcation explicit is what makes the wormhole a useful test bed rather than a slogan.