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Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017)

Couple the two boundaries of an eternal AdS black hole and the Einstein–Rosen bridge opens by a Planck-sized crack; nothing goes through faster than the coupling that opened it.

Kind: physics · Loophole: L3 · Standing: K4 · Bill: B-neg, B-boot · Last reviewed: 2026-09-12

The claim

Gao, Jafferis and Wall, JHEP 12 (2017) 151, take the eternal black hole in anti-de Sitter space, whose two exterior regions are joined by a non-traversable Einstein–Rosen bridge and whose holographic dual is the thermofield double state of two copies of a conformal field theory. They add to the Hamiltonian a small, time-dependent coupling between the two boundary theories, a "double trace deformation" $\delta S = \int dt\, d^{d-1}x\, h(t, x)\, \mathcal{O}_R(t, x)\, \mathcal{O}_L(-t, x)$, and compute the one-loop stress tensor of the bulk scalar dual to $\mathcal{O}$. The result: "we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein–Rosen bridge traversable" [HIGH] S1. A light ray sent in from one boundary early enough emerges at the other boundary after finite time. This is "the first such solution that has been shown to be embeddable in a UV complete theory of gravity" [HIGH] S1, because the deformation is a legitimate operation in the boundary theory and AdS/CFT guarantees its consistency in quantum gravity.

The claim is precise about what it is not. The abstract says in one sentence: "However, it cannot be used to violate causality" [HIGH] S1. The boundary theories are coupled by a direct interaction, which is a channel between the two sides in its own right; a signal through the bulk wormhole arrives no sooner than causality in the coupled boundary theory permits, and the coupling fixes the relative time of the two mouths so that the Morris–Thorne–Yurtsever boost trick is unavailable. The authors suggest the effect "might be related to quantum teleportation" [HIGH] S1: pre-shared entanglement (the thermofield double, which is the bridge) plus a classical channel (the coupling) moves a quantum state from one side to the other. That is the strongest form of the claim, and it is a claim about the interior of black holes and the meaning of entanglement, not about fast travel.

Origin and lineage

The bridge is the AdS version of the Einstein–Rosen bridge; its reading as the thermofield double is Maldacena (2003), and its reading as entanglement made geometric is ER = EPR, which the paper cites as the interpretive frame. The no-go results the paper has to get past are topological censorship and the achronal averaged null energy condition, the modern form of ENE-2, plus the generalised second law for causal horizons. Maldacena, Stanford and Yang, "Diving into traversable wormholes" (2017), developed the nearly-AdS$_2$ version, the teleportation reading and the bound on how much information can be sent [HIGH] S1. Maldacena and Qi (2018) built an eternal version with a time-independent coupling and matched it to two coupled SYK models [HIGH] S2. Maldacena, Milekhin and Popov 2018 carried the mechanism to four asymptotically flat dimensions with the coupling generated by field exchange rather than put in by hand. Fu, Grado-White and Marolf (2019) built asymptotically flat versions with cosmic strings [HIGH] S2. Jafferis et al. (Nature 612, 51, 2022) ran a learned SYK-like Hamiltonian on a quantum processor and reported traversable-wormhole teleportation dynamics, a claim disputed by Kobrin, Schuster and Yao (2023) [MED] S1.

The mechanism

Setup. The bulk is the eternal BTZ black hole (the paper works in $d = 2$ boundary dimensions, $D = 3$ bulk, and expects the same in higher $D$), with Kruskal coordinates $U$, $V$ and the future and past horizons at $V = 0$ and $U = 0$. The thermofield double state $|{\rm tfd}\rangle$ is invariant under $H_R - H_L$, which is the bulk boost Killing symmetry. The relevant deformation, with $\mathcal{O}$ of dimension $\Delta < d/2$, is turned on at boundary time $t_0$ [HIGH] S1 (§1).

Traversability criterion. Linearising the Einstein equation around the background at $V = 0$ and integrating over the affine parameter $U$ along the horizon, the total-derivative terms drop and

$$8\pi G_N \int dU\, T_{UU} = \frac{(d-2)}{4}\left[(d-3) r_h^{-2} + (d-1)\ell^{-2}\right]\int dU\, h_{UU},$$

where $r_h$ is the horizon radius and $\ell$ the AdS length [HIGH] S1 (eq. 1.4). The null ray from the past horizon is displaced to $V(U) = -(2 g_{UV}(0))^{-1}\int_{-\infty}^{U} dU\, h_{UU}$, so if the averaged null energy along the horizon is negative, $V(+\infty) < 0$ and "a light ray from left boundary will hit the right boundary after finite time" [HIGH] S1 (eq. 1.5). The throat is marginally traversable exactly when the averaged null energy condition is violated on the horizon generators.

Why decoupled systems cannot do it. In the decoupled theory $H_L + H_R$, no operator on the left can influence the right, so no state can be traversable without contradicting AdS/CFT. The paper shows this directly: $\int dU\, T_{UU}\,|{\rm tfd}\rangle$ is annihilated because it would have to be an eigenvector of the Hermitian operator $H_R - H_L$ with eigenvalue $-i$ [HIGH] S1 (§1). Any perturbation of the state alone lengthens the throat. The coupling between the boundaries is what changes the boundary conditions of the bulk scalar so that part of a wave hitting one boundary re-emerges from the other; the negative energy "is similar to the Casimir effect, since the interaction between the boundaries implies that the radial direction is effectively a compact circle" [HIGH] S1.

The computed stress tensor. The modified bulk two-point function is computed to first order in $h$, the one-loop $T_{UU}$ on the horizon is evaluated by point splitting, and its integral is found to be negative for all $0 < \Delta < 1$ with the appropriate sign of $h$; turning the coupling on earlier gives a larger effect, and the integral stays negative even where $T_{UU}$ itself turns positive at late times [HIGH] S1 (§3, Fig. 3.2).

How far it opens. The wormhole opens by

$$\Delta V \sim \frac{h\, G_N}{R^{D-2}}$$

in units $\hbar = 1$, where $R$ is the common scale of $r_h$, $\ell$ and the duration of the coupling [HIGH] S1 (eq. 5.1). "The wormhole is only open for a small proper time in the interior region" [HIGH] S1. Freivogel, Galante, Nikolakopoulou and Rotundo later quantified this: the wormhole is open for a proper time shorter than the Planck time, and for black holes of AdS size information cannot be reliably sent, while black holes much larger than the AdS radius can pass a number of quanta of order the horizon area in AdS units [HIGH] S1 (abstract). A quantum crossing is blueshifted to frequency $1/\Delta V$ in the Kruskal frame; the paper estimates the centre-of-mass energy of its collision with the negative-energy pulse and argues the eikonal approximation holds provided the particle is sent no earlier than about $\frac{3}{2}\Delta t$ with $\Delta t \approx R \ln(R / h L_{\rm Planck})$ before the coupling, which for $h \sim 1$ is of order the scrambling time [HIGH] S1 (§5).

Why it is not a shortcut. "A (test) astronaut from one boundary can only go through the wormhole before it closes, and she reaches the other boundary long after the boundary-boundary interaction is turned on" [HIGH] S1. The coupling breaks the $H_L - H_R$ symmetry, so "there is no way to boost her back to a time before she entered the worm hole. Thus the way we glue the two boundaries fixes the relative time coordinate between them, excluding the possibility of having closed time-like curves" [HIGH] S1 (§5). In the boundary theory the whole process is unitary evolution of two systems with a local-in-time coupling, which is causal by construction. Maldacena, Stanford and Yang make the information-theoretic content explicit: the protocol is teleportation, the coupling needs classical information sent from one side to the other, and the number of qubits that can pass is bounded by the coupling strength, $g \lesssim N_{\rm bits}$ [HIGH] S1 (eq. 2.21).

Energy and entropy. With the sign that opens the wormhole, the energy on each side decreases at linear order in $h$, and by the first law of entanglement the entanglement entropy between the two boundaries decreases too; the quantum extremal surface moves from the original bifurcation surface to the point where the two future horizons cross [HIGH] S1 (§4).

The headline number is $\Delta V \sim h G_N / R^{D-2}$: a Planck-suppressed opening, for a Planck-short proper time, at a boundary time long after the coupling.

What it costs

B-neg. Negative averaged null energy along the horizon generators is the necessary and sufficient condition for traversability in the linearised analysis, and the paper supplies it. The negative energy comes from an ordinary quantum field under modified boundary conditions, Casimir-like, so there is no exotic matter to manufacture; but it is energy-condition violation and the catalogue prices it as such. The averaged null energy condition is violated only on non-achronal geodesics, which is why the achronal-ANEC theorems are not contradicted [HIGH] S1.

B-boot. The wormhole opens only if the two boundaries are directly coupled, and the coupling is a channel between the two sides that must be in place before anything can cross. Whatever goes through arrives after the classical information carried by the coupling, which is the wormhole form of the CON-2 demand that the route be laid at sublight speed in advance. In the boundary theory there is no "through"; there is only the coupling.

There is no B-caus, because the coupling fixes the relative time of the mouths; no B-mass, because the construction is perturbative in $h$; and no B-new, because the ingredients are an ordinary CFT and Einstein gravity in AdS. The bill is small because the result is small: a bridge open for less than a Planck time.

Constraint scoring

ConstraintVerdictNote
CAU-1SATISFIESThe signal through the bulk arrives no earlier than the coupled boundary theory allows, and the boundary evolution is unitary and causal; the astronaut emerges long after the coupling was switched on, so no frame sees the effect precede its cause.
CAU-2SATISFIESNo closed timelike curves form; the coupling fixes the relative time coordinate of the two boundaries and the authors show the boost trick is unavailable.
CAU-3SATISFIESThe conversion by boosting one mouth is explicitly excluded because the deformation breaks the $H_L - H_R$ symmetry; this is a wormhole that cannot be made a time machine.
CAU-4N/ANo faster-than-light sector exists for which a preferred frame would need to be picked; the coupling itself is a boundary channel, not a superluminal one.
CAU-5SATISFIESThe teleportation reading needs the coupling as its classical channel; entanglement alone (the undeformed thermofield double) transmits nothing, in agreement with the no-communication theorem.
ENE-1VIOLATESThe averaged null energy along the horizon generators is negative by construction; this is the condition for opening and the paper computes it.
ENE-2SATISFIESThere is no time advance relative to the outside (the boundary), so the Olum and Gao–Wald theorems are not contradicted; the negative energy lives on non-achronal null geodesics, which the achronal theorems do not cover.
ENE-3SILENTThe quantum inequalities are derived for free fields in flat space with timelike sampling; the paper does not address them, and whether they bound a one-loop AdS stress tensor under a boundary coupling is not settled in the literature.
ENE-4N/AThe pocket geometry is a warp-bubble device with no counterpart.
ENE-5N/ANot a Natário-class warp metric.
ENE-6SATISFIESThe negative energy is Casimir-like in origin and magnitude, and the opening it buys is Planck-suppressed, consistent with the register's point that Casimir-scale negative energy buys nothing usable.
ENE-7SATISFIESThis is the register's named escape hatch. The negative averaged null energy sits on the horizon generators, which stop being achronal once the boundaries are coupled, so the achronal ANEC survives, and a signal through the bulk arrives no sooner than the direct boundary coupling allows: traversable, not a shortcut. The setting is anti-de Sitter, but the paper obeys the theorem's content rather than escaping its hypotheses.
CON-1N/ANo bubble wall; the horizons are those of the AdS black hole and the traversal is a perturbation of them.
CON-2SATISFIESThe two-sided coupling must be set up and switched on before anything can cross, and the traversal arrives after the coupling's own classical signal; the route is infrastructure laid in advance, as CON-2 demands.
CON-3N/ANo Krasnikov-type pre-laid metric.
STA-1N/ANo superluminal bubble wall; the semiclassical calculation here is under perturbative control at first order in $h$.
STA-2VIOLATESThe throat is opened by matter with negative averaged null energy, as STA-2 says every traversable throat must be; here the exotic ingredient is a quantum field under a boundary coupling rather than classical exotic matter.
STA-3SATISFIESNo chronology horizon forms because no time machine can be built from this wormhole.
HAZ-1N/ANo superluminal bubble sweeps up particles.
HAZ-2N/ANo bubble-wall Hawking bath; the traveller's hazard is the blueshifted collision with the negative-energy pulse, scored under HAZ-3.
HAZ-3VIOLATESThe opening $\Delta V \sim h G_N / R^{D-2}$ is Planck-scale and the wormhole is open for less than a Planck proper time (Freivogel et al.); a crossing quantum is blueshifted to $1/\Delta V$, so no macroscopic body passes, let alone one within a one-g tidal bound.
LOR-1SATISFIESNothing is accelerated to $c$; the traversing signal is a light ray or a quantum that follows a null geodesic of the perturbed geometry.
LOR-2N/ANo tachyonic matter.
LOR-3N/ANo group- or phase-velocity claim.
LOR-4N/ANo Scharnhorst-type effect.
WRP-1N/ANot a warp drive.
WRP-2N/AThe shell classification does not apply.
WRP-3N/AThe positive-energy warp argument does not bear on a wormhole.
MAN-1N/AThe AdS radial direction is the holographic dimension of the boundary theory, not an extra dimension offering a bulk shortcut; MAN-1's brane constructions are not involved.

Status of the argument

2016–2017: the paper appears on arXiv in August 2016 and in JHEP in December 2017; about 500 citations on INSPIRE as of 2026-09-12 [HIGH] S2. Maldacena, Stanford and Yang give the AdS$_2$ mechanics, the teleportation reading and the information bound within the year [HIGH] S1.

2018: Maldacena and Qi construct the eternal traversable wormhole with a constant coupling and its coupled-SYK dual [HIGH] S2. Maldacena, Milekhin and Popov build the four-dimensional asymptotically flat version, scored separately [HIGH] S1.

2019: Fu, Grado-White and Marolf construct asymptotically flat traversable wormholes with short transit times using cosmic strings and Hartle–Hawking quantum fields [HIGH] S2. Freivogel et al. bound the information transfer and find the opening shorter than a Planck time [HIGH] S1.

2022–2023: Jafferis et al. report "traversable wormhole dynamics on a quantum processor" using a machine-learned seven-Majorana Hamiltonian; Kobrin, Schuster and Yao argue the learned Hamiltonian does not reproduce SYK gravitational dynamics and that the signatures are explained without a wormhole; Nature published an erratum in 2025 [MED] S1. The dispute concerns the experiment, not the 2017 theory.

No peer-reviewed challenge to the Gao–Jafferis–Wall calculation itself exists as of 2026-09-12. The result is accepted as the demonstration that traversable wormholes are consistent with quantum gravity, and equally accepted as the demonstration that such a wormhole is not a shortcut.

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