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arxiv: 2605.05291 · v1 · submitted 2026-05-06 · ✦ hep-th

Recognition: unknown

Baby Universe in a Coupled SYK Model

Andrew Sontag , Herman Verlinde
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:26 UTC · model grok-4.3

classification ✦ hep-th
keywords SYK modelbaby universechord diagramsHartle-Hawking statedouble scaling limitentanglementAdS2saddle points
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The pith

The Hartle-Hawking chord state for the baby-universe saddle in a coupled SYK model exhibits genuine entanglement between the baby universe and external spacetimes.

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

This paper analyzes three saddle points of the partition function in the SYK model with a Maldacena-Qi coupling, taken in the double-scaling limit. The saddles are dual to three topologically distinct geometries: a pair of thermal disks, a cylinder, and a cylinder with a handle that represents a baby universe. The authors expand the effective G,Sigma action in powers of the coupling, reorganize the result as a sum of weighted chord diagrams, and then slice the diagrams open to obtain a Hilbert-space description on a spatial slice for each saddle. For the third saddle the resulting Hartle-Hawking state is entangled between the baby-universe handle and the two external regions, furnishing concrete evidence that a closed universe can carry a nontrivial quantum Hilbert space.

Core claim

The central claim is that the third saddle point, holographically dual to thermal AdS2 with a baby universe, produces a Hartle-Hawking chord state that is genuinely entangled between the baby universe and the external spacetimes. This state is constructed by deriving explicit chord rules from the power-series expansion of the effective G,Sigma action, expressing the partition function as a weighted sum of chord diagrams that probe the three bulk topologies, and slicing the diagrams to generate the spatial Hilbert space for each saddle.

What carries the argument

The chord-diagram representation obtained by expanding the G,Sigma action in powers of the coupling J and reorganizing into weighted diagrams; this representation spans the three bulk geometries and permits slicing to extract Hilbert-space states with entanglement for the handle topology.

Load-bearing premise

The power-series expansion of the effective G,Sigma action in the coupling, followed by the chord-diagram reorganization, correctly captures all saddle points and their associated bulk topologies, including the handle, without missing non-perturbative contributions or invalidating the double-scaling limit.

What would settle it

An explicit computation showing that the sliced chord state for the third saddle is a product state (zero entanglement between baby-universe and external legs) or that a non-perturbative evaluation of the partition function receives no contribution from the handle topology.

Figures

Figures reproduced from arXiv: 2605.05291 by Andrew Sontag, Herman Verlinde.

Figure 1
Figure 1. Figure 1: Schematic diagrams of the AS2 geometry in full Euclidean space (left panel) and with the top half Wick rotated to Lorentzian spacetime (right panel). The bottom boundary in each panel represents the Euclidean preparation of the two-sided CFT state dual to the dashed Cauchy slice Σ “ ΣL Y ΣB Y ΣR (the ΣB section continues past the brown line). This two-sided state is initialized by a heavy particle insertio… view at source ↗
Figure 2
Figure 2. Figure 2: Axis diagram representing which regions of inverse temperature β correspond to which geometric bulk phases of the coupled SYK model. Infinite temperature (β “ 0) is on the left edge. When β “ Opp 0 q, we have νβ “ µβ{p “ Op1{pq, so at J “ 0, ℓ00 and ℓ11 are both equal to their µ “ 0 values plus subleading corrections in p. The cross-site lengths ℓ01 and ℓ10 are both " Oppq. The standard DSSYK expansion in … view at source ↗
Figure 3
Figure 3. Figure 3: Plots of the free cylinder saddle point solution in the DSSYK-MQ model with νβ “ 15, for comparison to Figures 10 and 12 and also to Appendix C Figures 16 and 17. connects to the ribbon phase. Moving forward, we will use the term “cylinder phase” for the union of the tube phase and the ribbon phase. Between the tube phase and the disks phase lies a continuum of geometries interpolating between a progressiv… view at source ↗
Figure 4
Figure 4. Figure 4: One chord diagram contributing to the coupled SYK partition function in the disks phase. The green arcs on the left represent 00-chords and those on the right represent 11-chords. The diagram’s weight is computed by counting the numbers of chord nodes and intersections. 9 We need to take a little bit of care in this limit, since G01 “ Op1{pq is the same order as its variation. See Appendix B. 12 view at source ↗
Figure 5
Figure 5. Figure 5: One chord diagram contributing to the coupled SYK partition function in the ribbon phase. The green arcs anchored on the top represent 00-chords, and those anchored on the bottom represent 11-chords. The red lines represent 01-chords and 10-chords. The diagram’s weight is computed by counting the chord nodes on each boundary (7 each) as well as the total number of chord intersections on the cylinder (6). T… view at source ↗
Figure 6
Figure 6. Figure 6: The same chord diagram as in view at source ↗
Figure 7
Figure 7. Figure 7: Left: the same diagram as view at source ↗
Figure 8
Figure 8. Figure 8: One chord diagram contributing to the Hartle-Hawking state in the cylinder phase of the DSSYK-MQ model. The top line is half of the p0q boundary, and the the bottom line is half of the p1q boundary. The gray lines are the µ-chords, the purple line is the σ-chord, and the blue line is the maximally entangled state |1y. The orange lines are Hamiltonian chords, dropping the green/red designation from before s… view at source ↗
Figure 9
Figure 9. Figure 9: A very heavy matter particle’s creation and annihilation operators are placed along the top boundary of the cylinder geometry at opposite sides of the thermal circle. The heavy matter chord traveling along the cylinder (left) accumulates an exponential chord penalty of e ´∆ µβ{2 . For large enough ∆, a wormhole geometry forms (right) allowing the heavy matter chord to follow a more efficient route. 5.1 AS2… view at source ↗
Figure 10
Figure 10. Figure 10: Plot of the chord factor |Gab| for the AS2 saddle point with two heavy matter insertions, colored to match the terms in equations (5.5) and (5.6). The green diagonal ridge describes the short chords that connect nearby points on the (same or opposite) edge of the cylinder geometry. The blue peaks reveal the presence of a wormhole connecting the diametrically opposite points β{4 and 3β{4. The sharp-edged t… view at source ↗
Figure 11
Figure 11. Figure 11: Suggested bulk geometry dual to the free AS2 saddle point with two heavy matter insertions computed by (5.1) and plotted in view at source ↗
Figure 12
Figure 12. Figure 12: Plot of the chord factor |Gab| for the AS2 saddle point with one heavy matter insertion, colored to match the terms in equations (5.5) and (5.12). The blue peaks reveal the presence of a wormhole connecting the diametrically opposite points β{4 and 3β{4. The lack of discontinuities compared to view at source ↗
Figure 13
Figure 13. Figure 13: Bulk geometry dual to the AS2 saddle point with one heavy matter particle (indicated by the brown line) plotted in view at source ↗
Figure 14
Figure 14. Figure 14: One chord diagram contributing to the Hartle-Hawking state in the AS2 phase of the DSSYK-MQ model. The top and bottom lines are half of the p0q and p1q boundaries, respectively. The dashed lines are L, B, and R from left to right. The gray lines are the µ-chords, and the brown line is the single heavy O p0q worldline. The purple line is the ℓtube background chord. The maximally entangled state |1AS2 y liv… view at source ↗
Figure 15
Figure 15. Figure 15: Geometric parameters appearing in (A.16)-(A.21). All arcs are directional. The red, green, orange (ατ ), and blue (ασ) arcs are always directed from the primed to the unprimed coordinate. The purple arc (ζ) is always directed from a τ p1q to a σ p1q coordinate. In the crossed diagram, choosing “the other ατ ” or “the other ασ” is fine, but the ζ arc must always be that which overlaps with both ατ and ασ. … view at source ↗
Figure 16
Figure 16. Figure 16: Plots of xGaby in the free AS2 saddle point with two heavy operators. This solution is computed with νβ “ 15 and λ∆ “ p{5. The peak values of Gab near pβ{4, 3β{4q and p3β{4, β{4q indicate that this geometry contains a wormhole supported by the heavy particles’ worldlines. The sharp edges reflect the presence of the two heavy matter chords. can compute |G00p3β{4, β{4q| and then use (C.3) to solve for z. Th… view at source ↗
Figure 17
Figure 17. Figure 17: Plots of xGaby in the free AS2 saddle point with a single heavy matter chord. This solution is computed with νβ “ 15 and λ∆ “ p{2. We again clearly see the off-diagonal peak values that reveal the presence of the wormhole. Notice that G11 has no discontinuities away from τ “ τ 1 indicating that the dual geometry away from the heavy matter chord remains connected. for z “ c ` b c 2 ` 8p cosh2 ` νβ 2 ˘ c 4p… view at source ↗
read the original abstract

We analyze three saddle points of the path integral computing the partition function of the SYK model with a Maldacena-Qi coupling in the double scaling limit. The three saddle points are holographically dual to three topologically different spacetimes: a pair of Euclidean black holes (two thermal disks), a thermal AdS$_2$ (a cylinder), and a thermal AdS$_2$ with a baby universe (a cylinder with a handle). We develop explicit chord rules that span and probe these three bulk geometries. We derive the rules by expanding the effective $G,\Sigma$ action in powers of the coupling $\mathcal{J}$ and writing the partition function as a weighted sum of chord diagrams. By slicing the diagrams open, we generate a Hilbert space description on a spatial slice for each saddle point. The Hartle-Hawking chord state for the third saddle point has genuine entanglement between the baby universe and the external spacetimes, providing evidence that a closed universe can support a nontrivial Hilbert space.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes three saddle points of the path integral for the coupled SYK model in the double-scaling limit, holographically dual to two thermal disks, a thermal AdS2 cylinder, and a cylinder with a handle (baby universe). Chord rules are derived by expanding the effective G,Σ action in powers of the Maldacena-Qi coupling J, reorganizing the partition function as a sum of weighted chord diagrams, and slicing the diagrams to obtain a Hilbert-space description on a spatial slice for each saddle. The central claim is that the Hartle-Hawking chord state for the third saddle exhibits genuine entanglement between the baby universe and external spacetimes, providing evidence that a closed universe supports a nontrivial Hilbert space.

Significance. If the J-expansion and chord-diagram reorganization correctly capture the handle topology and associated entanglement without missing non-perturbative contributions, the result would supply concrete evidence for a Hilbert space on a closed baby universe via entanglement with external regions. This would be a notable advance in holographic models of baby universes and the emergence of closed-universe degrees of freedom, building on existing SYK chord-diagram techniques.

major comments (2)
  1. [Section deriving chord rules from G,Σ action expansion] Derivation of chord rules from the G,Σ action (section on perturbative expansion in J): The reorganization of the expanded effective action into weighted chord diagrams is asserted to span the three bulk geometries, including the handle. No explicit error estimates, truncation checks, or comparison against possible non-perturbative terms in the double-scaling limit are supplied to confirm that chord connectivity across the handle is fully captured; this directly affects whether the sliced Hartle-Hawking state exhibits the claimed entanglement.
  2. [Section on Hilbert space description via diagram slicing] Hilbert-space construction for the third saddle (section on diagram slicing and Hartle-Hawking state): The claim that the reduced density matrix on the spatial slice shows genuine entanglement between the baby universe and external spacetimes rests on the specific chord rules obtained from the expansion. Without an explicit computation of the reduced density matrix, an entanglement measure, or sample chord configurations illustrating handle-crossing chords, the evidence for a nontrivial Hilbert space remains unverified.
minor comments (2)
  1. [Abstract] The abstract states that 'explicit chord rules' are developed, yet the main text should clarify which rules are newly derived versus adapted from prior SYK literature to avoid ambiguity.
  2. [Introduction and notation] Notation for the double-scaling limit parameters and the precise definition of the Maldacena-Qi coupling J would benefit from an early dedicated equation to improve readability for readers outside the immediate SYK community.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Section deriving chord rules from G,Σ action expansion] Derivation of chord rules from the G,Σ action (section on perturbative expansion in J): The reorganization of the expanded effective action into weighted chord diagrams is asserted to span the three bulk geometries, including the handle. No explicit error estimates, truncation checks, or comparison against possible non-perturbative terms in the double-scaling limit are supplied to confirm that chord connectivity across the handle is fully captured; this directly affects whether the sliced Hartle-Hawking state exhibits the claimed entanglement.

    Authors: We appreciate the referee's emphasis on rigor in the perturbative expansion. The double-scaling limit organizes the J-expansion so that leading-order terms generate the chord diagrams for each topology, with the handle arising from specific contractions that connect across the baby-universe region. Higher-order and non-perturbative contributions are parametrically suppressed and do not modify the leading connectivity. To make this explicit, we will add a short discussion of truncation validity and error estimates in the revised manuscript. revision: yes

  2. Referee: [Section on Hilbert space description via diagram slicing] Hilbert-space construction for the third saddle (section on diagram slicing and Hartle-Hawking state): The claim that the reduced density matrix on the spatial slice shows genuine entanglement between the baby universe and external spacetimes rests on the specific chord rules obtained from the expansion. Without an explicit computation of the reduced density matrix, an entanglement measure, or sample chord configurations illustrating handle-crossing chords, the evidence for a nontrivial Hilbert space remains unverified.

    Authors: The slicing of the handle saddle produces chord diagrams containing connections that link the baby-universe interior to the exterior, rendering the Hartle-Hawking state non-factorizable by construction. While the manuscript presents the general structure, we agree an explicit illustration strengthens the claim. In the revision we will include a representative chord configuration with handle-crossing chords together with the corresponding reduced density matrix on a spatial slice and a direct computation of its entanglement entropy for a small number of chords. revision: yes

Circularity Check

0 steps flagged

No significant circularity; chord rules derived as output from G,Σ expansion

full rationale

The paper begins with the established effective G,Σ action of the coupled SYK model and performs a perturbative expansion in the Maldacena-Qi coupling J to obtain the weighted chord diagrams as an explicit output. These diagrams are then sliced to construct the Hilbert space states for each saddle, including the computation of entanglement in the cylinder-with-handle geometry. No step reduces the target result (entanglement in the Hartle-Hawking state) to a definition, a fitted parameter, or a self-citation chain; the chord rules and their topological interpretations are generated rather than presupposed. The derivation remains self-contained against the input action, with no load-bearing self-citations or ansatzes smuggled in.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard large-N saddle-point treatment of the SYK model, the validity of the double-scaling limit, and the assumption that the perturbative expansion in J generates all relevant chord diagrams for the handle topology. No new free parameters are introduced beyond the existing coupling J; the baby universe appears as an emergent geometric feature rather than an independently postulated entity.

axioms (2)
  • domain assumption The effective G,Sigma action of the coupled SYK model admits a reliable saddle-point expansion in the double-scaling limit.
    Invoked to justify reorganizing the partition function into chord diagrams corresponding to distinct bulk topologies.
  • domain assumption Chord diagrams obtained by slicing the perturbative expansion correctly encode the Hilbert space on a spatial slice for each saddle.
    Required to extract the Hartle-Hawking state and its entanglement properties from the diagrams.
invented entities (1)
  • Baby universe (handle on the cylinder) no independent evidence
    purpose: To label the third saddle-point geometry whose chord state exhibits entanglement with the exterior.
    The handle is generated by the chord-diagram sum rather than postulated independently; no separate falsifiable prediction (e.g., a new mass or coupling) is given outside the model.

pith-pipeline@v0.9.0 · 5466 in / 1655 out tokens · 22759 ms · 2026-05-08T17:26:59.689396+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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    q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.

Reference graph

Works this paper leans on

51 extracted references · 45 canonical work pages · cited by 1 Pith paper · 4 internal anchors

  1. [1]

    Eternal traversable wormhole

    Juan Maldacena and Xiao-Liang Qi. “Eternal traversable wormhole”. In: (Apr. 2018). arXiv: 1804.00491 [hep-th]

    work page Pith review arXiv 2018

  2. [2]

    Firewalls from wormholes

    Douglas Stanford and Zhenbin Yang. “Firewalls from wormholes”. In: (Aug. 2022). arXiv:2208. 01625 [hep-th]

    2022

  3. [3]

    Firewalls at exponentially late times

    Andreas Blommaert, Chang-Han Chen, and Yasunori Nomura. “Firewalls at exponentially late times”. In:JHEP10 (2024), p. 131.doi:10 . 1007 / JHEP10(2024 ) 131. arXiv:2403 . 07049 [hep-th]

    2024

  4. [4]

    On the non-perturbative bulk Hilbert space of JT gravity,

    Luca V. Iliesiu, Adam Levine, Henry W. Lin, Henry Maxfield, and M´ ark Mezei. “On the non- perturbative bulk Hilbert space of JT gravity”. In:JHEP10 (2024), p. 220.doi:10 . 1007 / JHEP10(2024)220. arXiv:2403.08696 [hep-th]

    work page arXiv 2024

  5. [5]

    The black hole interior from non-isometric codes and complexity

    Chris Akers, Netta Engelhardt, Daniel Harlow, Geoff Penington, and Shreya Vardhan. “The black hole interior from non-isometric codes and complexity”. In:JHEP06 (2024), p. 155.doi: 10.1007/JHEP06(2024)155. arXiv:2207.06536 [hep-th]

    work page doi:10.1007/jhep06(2024)155 2024

  6. [6]

    Observer complementarity for black holes and holography

    Netta Engelhardt, Elliott Gesteau, and Daniel Harlow. “Observer complementarity for black holes and holography”. In: (July 2025). arXiv:2507.06046 [hep-th]

    work page arXiv 2025

  7. [7]

    On observers in holographic maps

    Chris Akers, Gracemarie Bueller, Oliver DeWolfe, Kenneth Higginbotham, Johannes Reinking, and Rudolph Rodriguez. “On observers in holographic maps”. In:JHEP05 (2025), p. 201.doi: 10.1007/JHEP05(2025)201. arXiv:2503.09681 [hep-th]

    work page doi:10.1007/jhep05(2025)201 2025

  8. [8]

    Abdalla, S

    Ahmed I. Abdalla, Stefano Antonini, Luca V. Iliesiu, and Adam Levine. “The gravitational path integral from an observer’s point of view”. In:JHEP05 (2025), p. 059.doi:10 . 1007 / JHEP05(2025)059. arXiv:2501.02632 [hep-th]

    work page arXiv 2025

  9. [9]

    Towards a microscopic description of de Sitter dynamics

    Vladimir Narovlansky. “Towards a microscopic description of de Sitter dynamics”. In: (June 2025). arXiv:2506.02109 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  10. [10]

    A microscopic realization of dS 3

    Scott Collier, Lorenz Eberhardt, and Beatrix M¨ uhlmann. “A microscopic realization of dS 3”. In: SciPost Phys.18.4 (2025), p. 131.doi:10.21468/SciPostPhys.18.4.131. arXiv:2501.01486 [hep-th]

    work page doi:10.21468/scipostphys.18.4.131 2025

  11. [11]

    Tietto and H

    Damiano Tietto and Herman Verlinde. “A microscopic model of de Sitter spacetime with an observer”. In: (Feb. 2025). arXiv:2502.03869 [hep-th]

    work page arXiv 2025

  12. [12]

    Tommaso Marini, Xiao-Liang Qi, and Herman Verlinde.3D near-de Sitter gravity and the soft mode of DSSYK. 2026. arXiv:2604.21014 [hep-th].url:https://arxiv.org/abs/2604. 21014

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  13. [13]

    Cosmology from random entanglement

    Stefano Antonini, Martin Sasieta, and Brian Swingle. “Cosmology from random entanglement”. In:JHEP11 (2023), p. 188.doi:10.1007/JHEP11(2023)188. arXiv:2307.14416 [hep-th]

    work page doi:10.1007/jhep11(2023)188 2023

  14. [14]

    Antonini and P

    Stefano Antonini and Pratik Rath. “Do holographic CFT states have unique semiclassical bulk duals?” In: (Aug. 2024). arXiv:2408.02720 [hep-th]. 45

    work page arXiv 2024

  15. [15]

    Sasieta, B

    Martin Sasieta, Brian Swingle, and Alejandro Vilar L´ opez. “Baby Universes from Thermal Pure States in SYK”. In: (Nov. 2025). arXiv:2512.00149 [hep-th]

    work page arXiv 2025

  16. [16]

    The Large N Limit of Superconformal Field Theories and Supergravity

    Juan Martin Maldacena. “The Large N limit of superconformal field theories and supergravity”. In:Adv. Theor. Math. Phys.2 (1998), pp. 231–252.doi:10 . 1023 / A : 1026654312961. arXiv: hep-th/9711200

    work page internal anchor Pith review arXiv 1998

  17. [17]

    Anti de Sitter space and holography,

    Edward Witten. “Anti de Sitter space and holography”. In:Adv. Theor. Math. Phys.2 (1998), pp. 253–291.doi:10.4310/ATMP.1998.v2.n2.a2. arXiv:hep-th/9802150

    work page doi:10.4310/atmp.1998.v2.n2.a2 1998

  18. [18]

    Gauge Theory Correlators from Non-Critical String Theory

    S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov. “Gauge theory correlators from noncritical string theory”. In:Phys. Lett. B428 (1998), pp. 105–114.doi:10 . 1016 / S0370 - 2693(98)00377-3. arXiv:hep-th/9802109

    work page internal anchor Pith review arXiv 1998

  19. [19]

    A no-go theorem for largeNclosed universes

    Elliott Gesteau. “A no-go theorem for largeNclosed universes”. In: (Sept. 2025). arXiv:2509. 14338 [hep-th]

    2025

  20. [20]

    Engelhardt and E

    Netta Engelhardt and Elliott Gesteau. “Further Evidence Against a Semiclassical Baby Universe in AdS/CFT”. In: (Apr. 2025). arXiv:2504.14586 [hep-th]

    work page arXiv 2025

  21. [21]

    Kudler-Flam and E

    Jonah Kudler-Flam and Edward Witten. “Emergent Mixed States for Baby Universes and Black Holes”. In: (Oct. 2025). arXiv:2510.06376 [hep-th]

    work page arXiv 2025

  22. [22]

    Towards a holographic description of closed universes

    Hong Liu. “Towards a holographic description of closed universes”. In: (Sept. 2025). arXiv:2509. 14327 [hep-th]

    2025

  23. [23]

    Hong Liu.”Filtering” CFTs at large N: Euclidean Wormholes, Closed Universes, and Black Hole Interiors. 2025. arXiv:2512.13807 [hep-th].url:https://arxiv.org/abs/2512.13807

    work page arXiv 2025

  24. [24]

    Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information

    Donald Marolf and Henry Maxfield. “Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information”. In:JHEP08 (2020), p. 044. doi:10.1007/JHEP08(2020)044. arXiv:2002.08950 [hep-th]

    work page doi:10.1007/jhep08(2020)044 2020

  25. [25]

    McNamara and C

    Jacob McNamara and Cumrun Vafa. “Baby Universes, Holography, and the Swampland”. In: (Apr. 2020). arXiv:2004.06738 [hep-th]

    work page arXiv 2020

  26. [26]

    Xi Dong, Maciej Kolanowski, Xiaoyi Liu, Donald Marolf, and Zhencheng Wang.Null states and time evolution in a toy model of black hole dynamics. 2024. arXiv:2405.04571 [hep-th].url: https://arxiv.org/abs/2405.04571

    work page arXiv 2024

  27. [27]

    Antonini, P

    Stefano Antonini, Pratik Rath, Martin Sasieta, Brian Swingle, and Alejandro Vilar L´ opez. “The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes”. In: (July 2025). arXiv:2507.10649 [hep-th]

    work page arXiv 2025

  28. [28]

    Mykhaylo Usatyuk and Ying Zhao.Closed universes, factorization, and ensemble averaging. 2025. arXiv:2403.13047 [hep-th].url:https://arxiv.org/abs/2403.13047

    work page arXiv 2025

  29. [29]

    Closed universes in two dimensional gravity

    Mykhaylo Usatyuk, Zi-Yue Wang, and Ying Zhao. “Closed universes in two dimensional gravity”. In:SciPost Physics17.2 (Aug. 2024).issn: 2542-4653.doi:10.21468/scipostphys.17.2.051. url:http://dx.doi.org/10.21468/SciPostPhys.17.2.051

    work page doi:10.21468/scipostphys.17.2.051 2024

  30. [30]

    Harlow, M

    Daniel Harlow, Mykhaylo Usatyuk, and Ying Zhao. “Quantum mechanics and observers for grav- ity in a closed universe”. In: (Jan. 2025). arXiv:2501.02359 [hep-th]. 46

    work page arXiv 2025

  31. [31]

    Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

    Micha Berkooz, Prithvi Narayan, and Joan Simon. “Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction”. In:JHEP08 (2018), p. 192.doi:10.1007/JHEP08(2018)

    work page doi:10.1007/jhep08(2018 2018

  32. [32]

    arXiv:1806.04380 [hep-th]

    work page Pith review arXiv

  33. [33]

    Towards a full solution of the large N double-scaled SYK model

    Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, and Genis Torrents. “Towards a full solution of the large N double-scaled SYK model”. In:JHEP03 (2019), p. 079.doi:10.1007/ JHEP03(2019)079. arXiv:1811.02584 [hep-th]

    work page Pith review arXiv 2019

  34. [34]

    Semiclassical geometry in double- scaled SYK

    Akash Goel, Vladimir Narovlansky, and Herman Verlinde. “Semiclassical geometry in double- scaled SYK”. In:JHEP11 (2023), p. 093.doi:10.1007/JHEP11(2023)093. arXiv:2301.05732 [hep-th]

    work page doi:10.1007/jhep11(2023)093 2023

  35. [35]

    A symmetry algebra in double-scaled SYK

    Henry W. Lin and Douglas Stanford. “A symmetry algebra in double-scaled SYK”. In:SciPost Phys.15.6 (2023), p. 234.doi:10.21468/SciPostPhys.15.6.234. arXiv:2307.15725 [hep-th]

    work page doi:10.21468/scipostphys.15.6.234 2023

  36. [36]

    Susskind,De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit,2209.09999

    Leonard Susskind. “De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit”. In:JHAP5.1 (2025), pp. 1–30.doi:10 . 22128 / jhap . 2024 . 920 . 1103. arXiv:2209.09999 [hep-th]

    work page arXiv 2025

  37. [37]

    Rahman,dS JT Gravity and Double-Scaled SYK,2209.09997

    Adel A. Rahman. “dS JT Gravity and Double-Scaled SYK”. In: (Sept. 2022). arXiv:2209.09997 [hep-th]

    work page arXiv 2022

  38. [38]

    Double-scaled SYK and de Sitter holography,

    Vladimir Narovlansky and Herman Verlinde. “Double-scaled SYK and de Sitter holography”. In: JHEP05 (2025), p. 032.doi:10.1007/JHEP05(2025)032. arXiv:2310.16994 [hep-th]

    work page doi:10.1007/jhep05(2025)032 2025

  39. [39]

    Double-scaled SYK, chords and de Sitter gravity

    Herman Verlinde. “Double-scaled SYK, chords and de Sitter gravity”. In:JHEP03 (2025), p. 076. doi:10.1007/JHEP03(2025)076. arXiv:2402.00635 [hep-th]

    work page doi:10.1007/jhep03(2025)076 2025

  40. [40]

    SYK correlators from 2D Liouville-de Sitter gravity

    Herman Verlinde and Mengyang Zhang. “SYK correlators from 2D Liouville-de Sitter gravity”. In:JHEP05 (2025), p. 053.doi:10.1007/JHEP05(2025)053. arXiv:2402.02584 [hep-th]

    work page doi:10.1007/jhep05(2025)053 2025

  41. [41]

    The dilaton gravity hologram of double-scaled SYK

    Andreas Blommaert, Thomas G. Mertens, and Jacopo Papalini. “The dilaton gravity hologram of double-scaled SYK”. In:JHEP06 (2025), p. 050.doi:10.1007/JHEP06(2025)050. arXiv: 2404.03535 [hep-th]

    work page doi:10.1007/jhep06(2025)050 2025

  42. [42]

    Blommaert, D

    Andreas Blommaert, Damiano Tietto, and Herman Verlinde. “SYK collective field theory as complex Liouville gravity”. In: (Sept. 2025). arXiv:2509.18462 [hep-th]

    work page arXiv 2025

  43. [43]

    A cordial introduction to double scaled SYK

    Micha Berkooz and Ohad Mamroud. “A cordial introduction to double scaled SYK”. In:Rept. Prog. Phys.88.3 (2025), p. 036001.doi:10 . 1088 / 1361 - 6633 / ada889. arXiv:2407 . 09396 [hep-th]

    2025

  44. [44]

    The bulk Hilbert space of double scaled SYK

    Henry W. Lin. “The bulk Hilbert space of double scaled SYK”. In:Journal of High Energy Physics2022.11 (Nov. 2022).issn: 1029-8479.doi:10 . 1007 / jhep11(2022 ) 060.url:http : //dx.doi.org/10.1007/JHEP11(2022)060

    work page doi:10.1007/jhep11(2022)060 2022

  45. [45]

    The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual

    Alexei Kitaev and S. Josephine Suh. “The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual”. In:JHEP05 (2018), p. 183.doi:10.1007/JHEP05(2018)183. arXiv:1711.08467 [hep-th]. 47

    work page doi:10.1007/jhep05(2018)183 2018

  46. [46]

    Remarks on the Sachdev-Ye-Kitaev model

    Juan Maldacena and Douglas Stanford. “Remarks on the Sachdev-Ye-Kitaev model”. In:Phys. Rev. D94.10 (2016), p. 106002.doi:10 . 1103 / PhysRevD . 94 . 106002. arXiv:1604 . 07818 [hep-th]

    2016

  47. [47]

    Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK

    Akash Goel, Ho Tat Lam, Gustavo J. Turiaci, and Herman Verlinde. “Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK”. In:JHEP02 (2019), p. 156.doi: 10.1007/JHEP02(2019)156. arXiv:1807.03916 [hep-th]

    work page doi:10.1007/jhep02(2019)156 2019

  48. [48]

    Observers seeing gravitational Hilbert spaces: abstract sources for an abstract path integral

    Hong Zhe Chen. “Observers seeing gravitational Hilbert spaces: abstract sources for an abstract path integral”. In: (May 2025). arXiv:2505.15892 [hep-th]

    work page arXiv 2025

  49. [49]

    Daniel Harlow and Daniel Jafferis.The Factorization Problem in Jackiw-Teitelboim Gravity. 2019. arXiv:1804.01081 [hep-th].url:https://arxiv.org/abs/1804.01081

    work page arXiv 2019

  50. [50]

    Rabinovici, A

    E. Rabinovici, A. S´ anchez-Garrido, R. Shir, and J. Sonner.A bulk manifestation of Krylov com- plexity. 2023. arXiv:2305.04355 [hep-th].url:https://arxiv.org/abs/2305.04355

    work page arXiv 2023

  51. [51]

    The entanglement wedge of unknown couplings

    Ahmed Almheiri and Henry W. Lin. “The entanglement wedge of unknown couplings”. In:JHEP 08 (2022), p. 062.doi:10.1007/JHEP08(2022)062. arXiv:2111.06298 [hep-th]. 48

    work page doi:10.1007/jhep08(2022)062 2022