On tests for baby universes in AdS/CFT

Kenneth Higginbotham

REVIEW 3 major objections 5 minor 2 cited by

On tests for baby universes in AdS/CFT

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A boundary swap test cannot distinguish a baby universe from a no-baby bulk state, so semiclassical baby universes survive in AdS/CFT.

desk verdict A clean but conditional construction: the swap-test conclusion only follows if a post-selection state χ exists for the AR states, and that existence is assumed, not derived. read the letter →

arxiv 2507.05337 v2 pith:THZ3HABW submitted 2025-07-07 hep-th

Kenneth Higginbotham This is my paper

classification hep-th

keywords babyuniversesAdS/CFTholographicdictionaryswaptestpost-selectionnon-isometricmapsbulkreconstructionobserversinholography

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

A state in a conformal field theory (CFT) was previously shown to admit two equally valid bulk duals, one containing a baby universe and one not. A recent swap test concluded that the boundary dual of a bulk swap operator favors the no-baby state, under the assumption that the extrapolate dictionary defines a unique isometric holographic map. This paper argues that the extrapolate dictionary, the standard boundary-to-bulk reconstruction rule, does not fix a unique map for a closed universe because a baby universe has no asymptotic boundary. Post-selecting on the baby universe defines a second, non-isometric holographic map under which the same boundary operator has a different bulk dual whose expectation value exactly matches the no-baby prediction. The swap test therefore cannot distinguish the two candidate states, leaving semiclassical baby universes viable and opening the way to including observers in the baby universe.

What carries the argument

The load-bearing object is the second holographic map $V_{\text{baby}}$, defined by $V_{\text{baby}} \equiv |i|^{1/2}\, V_{\text{nb}} \otimes \langle\chi|_i$: it post-selects the entire baby-universe Hilbert space onto a fixed bra $\langle\chi|$, making the map non-isometric while keeping the extrapolate-dictionary action on the two asymptotic AdS components identical to $V_{\text{nb}}$. The induced operator map $V^*(O_{\partial}) = V^\dagger O_{\partial} V$ converts the boundary swap operator into $S_{\text{baby}} = |i|\, S \otimes |\chi\rangle\langle\chi|_i \otimes |\chi\rangle\langle\chi|_{i'}$, a swap on the AdS factors dressed by projectors on two copies of the baby universe. Trace cyclicity then forces the equality of expectation values, which is the entire argument.

What would settle it

A direct first-principles boundary computation of the swap expectation for the heavy-operator CFT state in a solvable model (for instance a two-dimensional dilaton-gravity theory or a large-N tensor model) would settle the claim: if it matches the naive baby-state value rather than the no-baby value, the equality fails. Alternatively, attempting to derive the post-selection state from the bulk path integral and finding no solution would collapse the construction.

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Extended reading notes

Core claim

The central claim is that the boundary operator $S_{\partial}$ has two consistent bulk duals. With the isometric no-baby map $V_{\text{nb}}$ it is the bulk swap operator $S$; with the new post-selecting map $V_{\text{baby}} = |i|^{1/2}\, V_{\text{nb}} \otimes \langle\chi|_i$ it is $S_{\text{baby}} = |i|\, S \otimes |\chi\rangle\langle\chi|_i \otimes |\chi\rangle\langle\chi|_{i'}$. The two maps are chosen so that $V_{\text{nb}}\,\psi^{(\text{nb})}\,V_{\text{nb}}^\dagger = V_{\text{baby}}\,\psi^{(\text{baby})}\,V_{\text{baby}}^\dagger$, and trace cyclicity then gives $\langle S_{\partial}\rangle = \langle S\rangle_{\psi^{(\text{nb})}} = \langle S_{\text{baby}}\rangle_{\psi^{(\text{baby})}}$. Measuring $S_{\partial}$ therefore does not amount to measuring the naive swap operator in the baby state, and the swap test does not favor the no-baby state. When the boundary state is entangled with an external reference, both the naive and the post-selected swap expectation values in the baby state are exponentially small, so the simplicity of $S_{\partial}$ cannot rule the baby state out either.

Load-bearing premise

The construction assumes, rather than derives, that there is a post-selection state in the baby-universe Hilbert space making the two holographic maps agree on the two candidate bulk states in question, with this state exhibited only in a toy qubit model with a trivial extrapolate dictionary.

Editorial extensions

If this is right

The boundary swap operator is not evidence against a semiclassical baby universe, because the same measurement is equally well described by the post-selected bulk operator in the baby state and by the original swap in the no-baby state.
The extrapolate dictionary is compatible with non-isometric, post-selecting holographic maps, so a closed universe does not need a uniquely defined boundary-to-bulk map.
When the CFT state is entangled with an external reference, both the naive and the post-selected swap expectation values in the baby state are exponentially small, making the two predictions indistinguishable to any simple experiment.
Applying observer-inclusion rules to $V_{\text{baby}}$ enlarges the fundamental Hilbert space to $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_I$, giving the baby universe non-trivial holographic content and new bulk operators.
The correct reading of the earlier swap-test result is the non-uniqueness of bulk reconstruction rather than the invalidity of the semiclassical baby universe.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The consistency condition relating the no-baby and baby states is imposed rather than derived; a first-principles derivation of the post-selection state from the bulk path integral would convert this consistency argument into a predictive dictionary.
The same post-selection logic should apply to other boundary operators, not just the swap operator; if it does, the holographic dictionary becomes state-dependent in a way that may conflict with boundary linearity in settings beyond this one.
Section 3's exponential-suppression mechanism suggests a concrete scaling test: entangle the boundary state with references of different sizes and locate the transition where the swap test loses its discriminating power.
If observers inside the baby universe have no equivalent description in the no-baby state, the observers themselves supply the extra data that resolves the uniqueness puzzle; the paper leaves this as an open question.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The short version: this paper gives a clean, conditional argument that a post-selected holographic map can make the EG swap test inconclusive, but the condition is doing all the work and isn't demonstrated. Section 2's algebra is fine. Define V_baby = |i|^{1/2} V_nb ⊗ ⟨χ|_i, and trace cyclicity gives ⟨O_∂⟩ = ⟨V_baby† O_∂ V_baby⟩. That part is unassailable. The physical content is the consistency condition (8), which is equivalent to demanding that a unit vector |χ⟩ exists such that ψ(nb) = |i| (1⊗⟨χ|)ψ(baby)(1⊗|χ⟩). That's a strong constraint on AR's specific states, and the paper simply assumes it. The toy qubit model evades the problem by setting V_nb = 1 and choosing χ to match the desired ψ(nb), which is circular.

Section 3 is softer still. The claim that a heavy operator's bulk excitation falls into the baby universe, so that the reference R purifies i alone, is a semiclassical assertion with no derivation. It might be true, but it isn't established.

What's genuinely new: the identification of S_baby as the dual of S_∂ under the post-selected map, and the observation that the same boundary operator can have two bulk duals with matching expectation values. That's a useful counterpoint to EG, and the connection to the observer program is timely. The citation pattern is unobjectionable, and the paper properly notes simultaneous related work [22].

This is for readers following the AR/EG debate in quantum gravity and holography. It deserves a serious referee because the question is important and the conditional logic is worth having on record. But it should come back with either a derivation of χ for the AR states or an explicit reframing as a consistency argument conditional on that existence. Section 3 needs more support. I wouldn't cite it as a settled result, but I'd send it out for review.

Referee Report

3 major / 5 minor

Summary. This paper challenges Engelhardt and Gesteau's recent swap-test evidence against semiclassical baby universes in AdS/CFT. The author proposes that the extrapolate dictionary does not uniquely define a holographic map: in addition to the isometric no-baby map V_nb, one may define a non-isometric baby-universe map V_baby = |i|^{1/2} V_nb ⊗ <χ|_i that post-selects on the baby universe. Under the consistency condition (8), restated as (9), the same boundary state Ψ(∂) is dual to both AR bulk states, and the boundary operator S_∂ acquires two bulk duals, S and S_baby, whose expectation values agree (Eq. (16)). Section 3 argues that when the boundary state is entangled with an external reference, the naive and non-perturbative swap predictions both become exponentially small, so the simplicity of S_∂ does not rule out the semiclassical baby state. Section 4 sketches how recent observer-in-holography rules could be applied to V_baby.

Significance. If the central consistency condition can be established for the actual AR states, the paper would substantially change the interpretation of the EG swap test: the boundary operator would no longer discriminate between the no-baby and baby bulk duals, and semiclassical baby universes would remain viable in at least some regimes. The formal traces leading to Eq. (16) are clean, and the qubit model usefully illustrates the role of post-selection. The paper also makes a concrete falsifiable claim: whenever Eq. (9) admits a solution |χ>, the EG test is non-discriminating; when it does not, the original EG conclusion is untouched. The main weakness is that the existence of |χ> and the Section 3 entanglement structure are assumed rather than derived, so the central claim is conditional on unproved inputs.

major comments (3)

[Section 2, Eqs. (8)-(9)] The central result (16) depends on the consistency condition V_nb ψ(nb) V_nb† = V_baby ψ(baby) V_baby†, which is imposed rather than demonstrated for the specific AR states. The paper does not prove that a unit vector |χ>_i satisfying Eq. (9) exists; projecting a generic pure baby state ψ(baby) onto a single baby-universe state |χ> yields a particular pure state on H_a⊗H_b, and there is no reason this state must coincide with ψ(nb) up to normalization. If no such |χ> exists, then no V_baby of the form (7) satisfies (8), the equality (16) fails, and the conclusion that S_∂ cannot distinguish the two bulk duals collapses. The qubit model in §2.1 does not fill this gap: with V_nb = 1, Eq. (20) simply sets |ψ(nb)> equal to the projected state |χ*>_ab, which is circular. The author should either prove the existence of |χ> for the actual AR states or state this as an explicit assumption and explain its physical origin.
[Section 3, Eqs. (22)-(24)] The claim that both the naive and non-perturbative swap expectation values become exponentially small in an entangled-reference regime rests on the unproved physical assertion that the heavy operator O^(k) causes the bulk excitation to fall into the baby universe, so that no entanglement exists between ab and R in the baby state. This is a dynamical semiclassical input, not a consequence of the post-selection map; the equality <S>_ψ(baby) = e^{-S_2(ab)} in Eq. (24) is asserted without derivation. If the reference R remains entangled with ab, the naive prediction need not be suppressed in the same way, and the simplicity argument in Section 3 would not apply. The author should derive this entanglement structure from AR's state preparation or identify the approximation under which it holds.
[Section 2, Eqs. (14)-(16)] Once V_baby is defined as in (7) and the consistency condition (8) is assumed, the equality (16) follows immediately from trace cyclicity; it is therefore a consistency condition rather than an independent test. The physical content lies entirely in the existence and correctness of V_baby for ψ(baby), and the paper should provide evidence that V_baby is the map selected by the extrapolate dictionary, rather than an arbitrary auxiliary construction. Without such evidence, the statement that S_∂ 'cannot distinguish' the two bulk states is a restatement of the imposed condition (8), not a new dynamical result.

minor comments (5)

[Section 2, Eq. (7)] The notation |i| = dim H_i is confusing because i also labels the baby universe; please use a distinct symbol such as d_i and define it at first use.
[Section 2, Eq. (8)] The approximate equality symbol ≈ in Eq. (8) is never specified; the author should state whether the equality is exact, or if approximate, in which norm or trace distance and with what tolerance.
[Section 2.1, Eq. (17)] The qubit model writes |ψ(baby)> = |Φ^+>_{a,i1} |Φ^+>_{b,i2}; please clarify the normalization conventions for the Bell states and the overall normalization of |ψ(baby)>.
[Section 3, after Eq. (22)] The notation S(ab) = S(R) and S_2(R) is introduced without defining the Renyi entropy convention; please define S_2 and explain why the no-baby entanglement entropy equals the reference entropy.
[Section 4, Eq. (25)] The sentence 'Either approach can be readily applied to V_baby' is a sketch; since the HUZ and Colorado rules differ, a brief description of how each rule modifies V_baby would make the claim more transparent.

Circularity Check

2 steps flagged · score 8.0 of 10

The swap-test non-distinguishability result is built into the definition of V_baby and the imposed consistency condition, not derived from AR's states.

self definitional [Section 2, Eqs. (7)-(9); toy model Section 2.1]
"Consistency with AR’s results [12] requires that both bulk states be mapped to the same boundary state Ψ(∂) by their respective holographic maps: Vnbψ(nb)V†nb ≈ Vbabyψ(baby)V†baby. (8) Using the fact that Vbaby acts as the isometry Vnb on the Ha ⊗ Hb subsystem, we find that this implies the following relationship between the two bulk states: ψ(nb) ≈ |i|(1ab ⊗ ⟨χ|i)ψ(baby)(1ab ⊗ |χ⟩i). (9)"

The map V_baby is defined in Eq. (7) with a free post-selection state |χ>. Equation (8) then imposes that V_baby and V_nb produce the same boundary state; Eq. (9) is merely this consistency condition restated as a constraint relating ψ(nb) and ψ(baby). No derivation is given that such a |χ> exists for AR's specific semiclassical states. The toy model in Section 2.1 makes the fitting explicit: the post-selection is chosen so that |χ*> equals the desired no-baby state. Thus the central relation on which all later results depend is imposed by construction, not derived from AR's state preparation or the extrapolate dictionary.
self definitional [Section 2, Eqs. (14)-(16)]
"Sbaby ≡(V†baby ⊗V†baby)S∂(Vbaby ⊗Vbaby) = |i| S ⊗ |χ⟩⟨χ|i ⊗ |χ⟩⟨χ|i′, (14) ... ⟨S∂⟩Ψ(∂) = ... = ⟨Sbaby⟩ψ(baby), (15) ... ⟨S∂⟩Ψ(∂) = ⟨S⟩ψ(nb) = ⟨Sbaby⟩ψ(baby). (16)"

Once S_baby is defined as the pullback of S_∂ through V_baby, Eq. (15) is the trace-cyclicity identity (10)-(11), which holds for any boundary operator and any holographic map. Equation (16) is therefore a tautology: it asserts that a boundary operator has a bulk dual with the same expectation value under each map, which is automatically true by the definition of the pullback. The only physical content—that V_baby actually maps ψ(baby) to Ψ(∂)—is exactly the assumed consistency condition (8)/(9), whose existence is never proven for AR's states. The paper itself later notes that the agreement is 'by construction,' confirming that the conclusion follows from the definition rather than from independent input.

full rationale

The paper's derivation of Eq. (16) is internally consistent, but the equality is not an empirical or first-principles result. V_baby is defined with an arbitrary post-selection |χ>; the consistency condition (8) is then imposed, forcing Eq. (9) to hold. No proof is given that a |χ> satisfying Eq. (9) exists for AR's specific semiclassical states. In the toy model, |χ> is reverse-engineered to reproduce the desired no-baby state, so the model is constructed to match the conclusion. Given V_baby, Eq. (14) defines S_baby as the pullback of S_∂, and Eq. (15) is an identity from trace cyclicity, valid for any map V. Thus Eq. (16) is true by construction, and the statement that S_∂ 'cannot distinguish' the two candidate bulk states is equivalent to the assumed consistency condition, not a consequence of the extrapolate dictionary alone. Section 3's reference-entanglement argument is a separate, non-circular calculation, but it does not provide independent evidence that V_baby is the correct holographic map for AR's states. The paper is transparent about the 'by construction' nature of the agreement, but transparency does not remove the circularity: the central claim reduces to the choice of |χ> and the imposed equality (8). No load-bearing self-citation chain is involved; the issue is definitional.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim is conditional on accepting a non-isometric post-selection map whose existence and consistency with AR's states are assumed rather than demonstrated. The main free parameter is the post-selection state |χ>, which is effectively chosen to force the two bulk states to map to the same boundary state. No new physical entities such as particles or forces are introduced.

free parameters (2)

Post-selection state |χ>_i = Not fixed; generic/random, but required to satisfy Eq (8) for AR's states
Introduced in Eq (7) and constrained by Eq (9) so the baby state maps to the same boundary state as the no-baby state. Its existence is assumed, not derived, and in the qubit model it is explicitly chosen to match the desired no-baby state.
Baby universe Hilbert space dimension |i| = Undetermined (prefactor |i|^{1/2} in Eq (7))
The dimension enters the normalization of V_baby and is stated to preserve normalization on average; it is not fixed by independent data.

assumptions (4)

domain assumption Post-selection on closed universes is a valid rule for holographic maps.
The paper relies on this from [8,10,20,21] to justify V_baby; it is not proven in this work. Invoked in Section 2 around Eq (7).
domain assumption The extrapolate dictionary cannot define a map on the baby universe because it lacks an asymptotic boundary, so post-selection is the only option.
Stated in the Introduction and Section 2; used to justify why V_baby can be non-isometric. This is an interpretation.
ad hoc to paper There exists a state |χ> such that the consistency condition (8) holds for AR's two bulk states.
Eq (8) is imposed to ensure both bulk states are dual to the same boundary state; the existence of |χ> is not demonstrated for the actual AR states, only in a toy model.
ad hoc to paper The heavy operator O^(k) in Eq (22) causes the bulk excitation to fall into the baby universe, leaving no entanglement between ab and R in the baby state.
Assumed in Section 3 to derive Eq (24); no dynamical model is provided.

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Cite this review

Pith. "Pith review of On tests for baby universes in AdS/CFT." pith.science (2026). https://pith.science/paper/THZ3HABW

@misc{pith2026250705337,
  author       = {Pith},
  title        = {Pith review of: On tests for baby universes in AdS/CFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/THZ3HABW}},
  note         = {Machine review of arXiv:2507.05337}
}

read the original abstract

To address a puzzle by Antonini and Rath -- where a single CFT state has two bulk duals, one with a baby universe and one without -- Engelhardt and Gesteau recently devised a test for baby universes in AdS/CFT. Using the extrapolate dictionary, they showed that the boundary dual of a bulk swap test favored bulk spacetimes without a baby universe, providing evidence against their semiclassical validity. However, recent work suggests that holographic maps should post-select on such closed universes, and we argue that this is consistent with the extrapolate dictionary. We therefore construct a new holographic map for bulk states with baby universes and use this to show that the swap test cannot distinguish between Antonini and Rath's two candidate bulk duals. This not only allows for a valid semiclassical description of the baby universe, but also enables the application of recent techniques for including observers in holographic maps.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Baby Universes from Thermal Pure States in SYK
hep-th 2025-11 conditional novelty 6.0 of 10

A JT-gravity baby universe is constructed with a microscopic dual given by a low-temperature thermal pure state of two coupled SYK models, and its bulk entanglement to the AdS region is O(N) below the phase transition.
The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes
hep-th 2025-07 conditional novelty 5.0 of 10

A closed universe in AdS/CFT is not ruled out by recent SWAP-test arguments; the one-dimensional Hilbert space seen from the CFT is external indistinguishability, and CFT data can reconstruct the closed universe's geometry.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [22]

Engelhardt, E

N. Engelhardt, E. Gesteau and D. Harlow,Observer complementarity for black holes and holography,2507.06046

arXiv

[2] [1]

Maldacena and L

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work page 2004

[3] [2]

Almheiri, R

A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao,The Page curve of Hawking radiation from semiclassical geometry,Journal of High Energy Physics2020(2020) 149 [1908.10996]

arXiv 2020

[4] [3]

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G. Penington, S.H. Shenker, D. Stanford and Z. Yang,Replica wormholes and the black hole interior,1911.11977

arXiv 1911

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D. Marolf and H. Maxfield,Transcending the ensemble: Baby universes, spacetime wormholes, and the order and disorder of black hole information,Journal of High Energy Physics2020(2020) 44

work page 2020

[6] [5]

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J. McNamara and C. Vafa,Baby Universes, Holography, and the Swampland, 2004.06738

arXiv 2004

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work page 2024

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Usatyuk and Y

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