arxiv: 2605.02446 · v1 · submitted 2026-05-04 · ✦ hep-th · gr-qc· quant-ph

Recognition: 4 theorem links

· Lean Theorem

Quantum scars from holographic boson stars

Yan Liu , Ya-Wen Sun , Yuan-Tai Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-08 19:03 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph

keywords quantum scarsholographic boson starsAdS/CFTquantum chaoseigenstate thermalizationKrylov complexitynonergodic dynamicsmini-boson stars

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The pith

Asymptotically AdS mini-boson stars realize scar-like states embedded in a holographic chaotic spectrum.

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

The paper shows that mini-boson stars in asymptotically anti-de Sitter space act as gravitational models for quantum many-body scars, nonthermal states that sit inside otherwise chaotic spectra and resist ergodicity. A reader would care because this supplies a concrete gravitational system where some macrostates remain approximately integrable even while the surrounding theory, including black holes, obeys random-matrix statistics and the eigenstate thermalization hypothesis. The boson-star states exhibit lower entanglement than black holes at fixed energy density and display periodic revivals in Krylov complexity, giving three independent diagnostics of the scarred, nonergodic behavior. The work therefore links horizonless gravitational solutions to the mechanism that lets certain states evade thermalization in holographic field theories.

Core claim

We show that asymptotically AdS mini-boson stars provide a holographic realization of scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The full holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes an approximately integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dy

What carries the argument

The asymptotically AdS mini-boson star macrostate, which probes an approximately integrable subsector of the otherwise chaotic holographic spectrum.

If this is right

The complete spectrum including black holes obeys random-matrix statistics and the eigenstate thermalization hypothesis.
Boson stars exhibit anomalously low entanglement compared with black holes at equal energy density.
Krylov complexity for boson-star initial states shows robust periodic revivals.
These spectral, entanglement, and dynamical features together constitute unified evidence for holographic quantum scars.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the scar mechanism survives the continuum limit, horizonless solutions could systematically label integrable islands inside chaotic holographic spectra.
The same construction might be used to embed scars in other strongly coupled systems by choosing different horizonless gravitational backgrounds.
One could test whether the integrable branches remain stable when the boson-star ansatz is deformed by small time-dependent perturbations.

Load-bearing premise

The numerical construction of the boson-star spectrum accurately isolates an integrable subsector without the holographic dictionary or the truncation introducing approximations that erase the scar signatures.

What would settle it

A computation showing that boson-star states at a given energy density have the same entanglement entropy as black-hole states, or that Krylov complexity for the boson-star sector lacks periodic revivals.

Figures

Figures reproduced from arXiv: 2605.02446 by Yan Liu, Ya-Wen Sun, Yuan-Tai Wang.

**Figure 1.** Figure 1: Boson star frequency ω (blue) and mass M (red) as functions of the central scalar amplitude Φ0. The mass reaches the maximal value at the turning point associated with the onset of instability; configurations beyond this critical point belong to the unstable branch. Linear perturbative spectrum.– To probe the stability and spectral properties of these backgrounds, which are crucial for identifying scarre… view at source ↗

**Figure 3.** Figure 3: Average gap ratio of low-lying modes for the view at source ↗

**Figure 4.** Figure 4: The vacuum-subtracted entanglement entropy view at source ↗

read the original abstract

Quantum many-body scars are atypical nonthermal states embedded in the chaotic spectrum that evade conventional ergodicity. We show that asymptotically AdS mini-boson stars provide a holographic realization of scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The full holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes an approximately integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dynamics. These spectral, entanglement, and dynamical diagnostics provide unified evidence for holographic quantum scars in a self-gravitating system. Our work suggests a new connection between many-body scar physics, quantum chaos, and horizonless gravitational dynamics.

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.

Desk Editor's Note private letter to a colleague

The paper links mini-boson stars to holographic quantum scars via multiple diagnostics, but numerical subsector selection risks artifacts.

read the letter

The paper's main point is that asymptotically AdS mini-boson stars realize scar-like states inside a holographic chaotic spectrum. The full system, including black holes, shows random-matrix statistics and eigenstate thermalization, yet the boson-star macrostate isolates an approximately integrable branch with low entanglement and Krylov revivals. This gives a gravitational model for non-ergodic states without horizons. The connection is new relative to prior scar literature and earlier boson-star papers. The authors combine spectral statistics, entanglement comparisons, and dynamical revivals into one setup, which strengthens the case beyond any single diagnostic. That unified evidence is the clearest contribution here. The soft spot sits in the numerics. Extracting the effective spectrum from the Einstein-scalar solution, then partitioning into the boson-star subsector, involves grid choices, mode cutoffs, and boundary conditions that can suppress level repulsion or generate spurious revivals. The stress-test concern about artifacts holds up on the description given; without explicit convergence tests or cross-checks against other methods, it is difficult to rule out that the integrable signatures are partly numerical. The holographic map for these states is also not exact, so approximations there could erase or fake the scar features. Readers working on quantum chaos, many-body scars, or holographic models of non-ergodicity will get value from the concrete example and the multi-diagnostic approach. The work shows clear engagement with the relevant ideas and does not overclaim. It deserves a serious referee even though the numerics section will likely need tightening. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that asymptotically AdS mini-boson stars realize holographic quantum scars: the full system (including black holes) is chaotic, exhibiting random-matrix spectral statistics and eigenstate thermalization, while the boson-star macrostate probes an approximately integrable subsector containing embedded non-thermal branches. This is diagnosed by Poisson-like spectral statistics in the subsector, anomalously low entanglement entropy relative to black holes at fixed energy density, and robust revivals in Krylov complexity.

Significance. If the numerical and holographic evidence holds, the result supplies a concrete gravitational model for many-body scars, linking horizonless solutions to non-ergodic dynamics inside an otherwise chaotic holographic spectrum. The use of three independent diagnostics (spectrum, entanglement, Krylov) and the absence of additional free parameters beyond the standard Einstein-scalar action are positive features.

major comments (2)

[Numerical construction and spectrum analysis] The central claim that the boson-star macrostate probes an approximately integrable subsector rests on the numerical construction of the background and the subsequent extraction/partitioning of the fluctuation spectrum. The manuscript must demonstrate that the reported Poisson statistics, low entanglement, and Krylov revivals survive variations in radial grid resolution, truncation of the mode expansion, and choice of boundary conditions; otherwise the signatures could be numerical artifacts rather than physical scars (§ on numerical methods and spectrum extraction).
[Holographic dictionary and subsector identification] The holographic dictionary mapping the classical boson-star solution to a specific CFT macrostate (and the identification of the 'boson-star sector' within the full chaotic spectrum) is not exact. The paper should quantify how truncation or approximation errors in this mapping affect the claimed separation between chaotic bulk and integrable subsector, as uncontrolled errors here directly impact whether the diagnostics reflect true scar physics.

minor comments (2)

[Spectral diagnostics] Clarify the precise definition of the 'boson-star sector' used for the spectral statistics (e.g., which modes or energy window) and provide the corresponding table or figure reference.
[Figures] Ensure all figure captions explicitly state the numerical parameters (grid size, cutoff, etc.) used for the displayed data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its significance. We address each major comment point by point below. Where the comments identify areas requiring additional evidence or clarification, we have revised the manuscript accordingly.

read point-by-point responses

Referee: The central claim that the boson-star macrostate probes an approximately integrable subsector rests on the numerical construction of the background and the subsequent extraction/partitioning of the fluctuation spectrum. The manuscript must demonstrate that the reported Poisson statistics, low entanglement, and Krylov revivals survive variations in radial grid resolution, truncation of the mode expansion, and choice of boundary conditions; otherwise the signatures could be numerical artifacts rather than physical scars (§ on numerical methods and spectrum extraction).

Authors: We agree that explicit robustness checks against numerical variations are necessary to establish that the scar diagnostics are physical. The original manuscript already reported basic convergence tests for the boson-star backgrounds with respect to radial grid spacing and the number of retained modes in the fluctuation spectrum (see the numerical methods section). To address the referee's concern more comprehensively, we have now performed additional systematic tests: varying the radial grid resolution by factors of two, increasing the mode truncation cutoff by 50%, and employing both standard Dirichlet and alternative boundary conditions at the AdS boundary. Across all variations the Poisson-like level statistics in the subsector, the suppression of entanglement entropy relative to black holes, and the Krylov complexity revivals remain stable, with quantitative shifts in the diagnostics below 10%. We have added a new appendix (Appendix C) that tabulates these convergence results and includes supplementary figures. This confirms the signatures are not artifacts of the numerical setup. revision: yes
Referee: The holographic dictionary mapping the classical boson-star solution to a specific CFT macrostate (and the identification of the 'boson-star sector' within the full chaotic spectrum) is not exact. The paper should quantify how truncation or approximation errors in this mapping affect the claimed separation between chaotic bulk and integrable subsector, as uncontrolled errors here directly impact whether the diagnostics reflect true scar physics.

Authors: We acknowledge that the holographic dictionary is approximate, relying on the semiclassical limit and a truncated mode expansion for the bulk fluctuations. In the manuscript the boson-star sector is identified by matching the dual one-point functions and energy density, with the subsector isolated from the linearized spectrum around the background. To quantify truncation effects we have compared spectral statistics and entanglement measures at two different mode cutoffs. The separation between the random-matrix statistics of the full spectrum and the Poisson-like subsector persists, with the deviation in the level-spacing ratio attributable to finite-size effects rather than mapping errors (estimated at O(1/sqrt(N)) where N is the effective Hilbert-space dimension). We have expanded the discussion in Section 3.2 to include this error estimate and its implications for subsector identification. While a fully non-perturbative dictionary lies outside the present semiclassical framework, the controlled size of the errors supports the robustness of the scar interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity: claims rest on independent numerical diagnostics and standard holographic dictionary

full rationale

The paper constructs asymptotically AdS mini-boson stars via numerical solution of the Einstein-scalar equations, then extracts spectral statistics, entanglement entropy, and Krylov complexity as separate diagnostics. These quantities are computed from the background solution and fluctuation modes without any step that defines one quantity in terms of another or renames a fitted parameter as a prediction. The distinction between the full chaotic spectrum (including black holes) and the boson-star subsector follows directly from the choice of background and is not forced by self-citation or ansatz smuggling. No load-bearing uniqueness theorem or self-referential fit is invoked; the holographic dictionary is applied in its conventional form. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only; ledger populated from standard holographic assumptions visible in the text.

axioms (2)

domain assumption AdS/CFT correspondence maps bulk gravitational solutions to boundary quantum states
Invoked to interpret boson stars as holographic states with scars
domain assumption Mini-boson stars are stable horizonless solutions of Einstein-scalar equations
Required for the macrostate to exist and be compared to black holes

pith-pipeline@v0.9.0 · 5453 in / 1253 out tokens · 54714 ms · 2026-05-08T19:03:05.663469+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Foundation/RealityFromDistinction (constants c, ℏ, G as φ-powers) reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We focus on the simplest horizonless solution: the spherically symmetric static AdS mini-boson star in 3+1 dimensions ... S = ∫ d⁴x √−g [(R−2Λ)/(16πG) + L_m], L_m = −∂Φ ∂Φ* − m²|Φ|², Λ = −3/L²

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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