arxiv: 2604.05815 · v1 · submitted 2026-04-07 · ✦ hep-th · gr-qc· quant-ph

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Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity

Ra\'ul Arias , Agust\'in Tamis

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:32 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph

keywords JT gravityisland saddlecapacity of entanglementreplica trickblack hole entropyvon Neumann entropysemiclassical gravityentanglement capacity

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The pith

Capacity of entanglement detects finite-n structure in the factorized island branch of JT gravity where entropy plateaus.

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

The paper studies the factorized island branch in Jackiw-Teitelboim gravity coupled to a large-c bath. It establishes that in the late-time high-temperature regime the von Neumann entropy reaches a plateau with no change at the first nontrivial correction, yet the capacity of entanglement acquires a definite correction from the surrounding replica geometry. A sympathetic reader would care because this supplies a controlled semiclassical setting in which the full replica saddle carries observable information beyond the n to 1 limit, showing that nearby replica data remain physically meaningful even when the entropy itself appears rigid.

Core claim

In the late-time high-temperature regime of the factorized island branch, the entropy plateau remains unchanged at the first nontrivial order while the capacity acquires a definite correction. This shows that the factorized island saddle already carries finite-n information beyond the entropy, and that the capacity is a natural observable for exposing it. The physics of island saddles is not exhausted by the n=1 limit; the surrounding replica geometry contains additional, and observable, information about how the semiclassical saddle is assembled.

What carries the argument

The capacity of entanglement evaluated on the factorized island saddle within the replica manifold of JT gravity coupled to a large-c bath.

Load-bearing premise

The factorized island branch remains the dominant saddle and the large-c bath approximation continues to control the capacity calculation at the order where the correction appears.

What would settle it

An explicit higher-order calculation in the JT model showing either a correction to the entropy plateau at the same order or a capacity correction whose size or sign differs from the predicted value.

Figures

Figures reproduced from arXiv: 2604.05815 by Agust\'in Tamis, Ra\'ul Arias.

**Figure 2.** Figure 2: Representative one-QES building block. (a) Lorentzian picture with a single radiation [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Conformal welding for the one-QES replicated geometry. The interior map [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: Numerical fit check of αmat(n): fitted points extracted from the quartic fit compared with the analytic expression (D.1). The agreement is excellent throughout the displayed range [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗

read the original abstract

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit $n \to 1$. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-$c$ bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-$n$ information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the $n=1$ limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

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 shows a correction to the capacity of entanglement in the factorized island branch of JT gravity where the entropy plateau holds at leading order, but the large-c control on the second n-derivative needs explicit checking.

read the letter

The main point is that in the late-time high-temperature regime of JT gravity coupled to a large-c bath, the factorized island saddle gives a nonzero correction to the capacity while the entropy stays flat at the first nontrivial order. This is new: earlier island calculations in JT focused on the von Neumann entropy from the n=1 limit, and this work extracts the second derivative of the Renyi entropy at n=1 from the same replica geometry to expose extra finite-n content that survives in the controlled branch. It supplies a clean semiclassical example that the surrounding replica data can be observable even when the entropy itself looks rigid. The setup stays inside the factorized branch and the large-c approximation, which keeps the calculation tractable and avoids more complicated saddles. That is a real strength for a technical note in this subfield. The soft spot is the one the stress-test flagged. Capacity involves the second derivative with respect to n, so any n-dependent piece in the on-shell action that is subleading for the entropy can become leading for the capacity. The abstract claims the correction is definite, which implies the authors checked that higher 1/c or fluctuation terms do not contaminate the result at the kept order. If the full text shows the explicit expansion and confirms the control, the claim holds; if it relies on the leading saddle without that check, the result is weaker than stated. This is for readers working on holographic islands, replica methods in JT gravity, or higher Renyi observables in quantum gravity. It is a modest but precise addition that identifies a new probe for saddle structure. I would send it to peer review because the central claim is well-posed and the setup is standard enough for referees to verify the derivative control in one pass.

Referee Report

1 major / 2 minor

Summary. The paper analyzes the capacity of entanglement in the factorized island branch of JT gravity coupled to a large-c bath. It claims that, in the late-time high-temperature regime, the von Neumann entropy plateau is unchanged at the first nontrivial order in the replica parameter, while the capacity acquires a definite correction arising from the surrounding replica geometry. This is presented as evidence that finite-n replica data remain physically meaningful even when the n=1 entropy appears rigid, and that the factorized island saddle encodes additional observable information beyond the entropy limit.

Significance. If the central result holds, the work supplies a controlled semiclassical example in which an observable sensitive to the second n-derivative distinguishes replica structure invisible to the entropy alone. This strengthens the case for treating island saddles as carrying finite-n information and identifies the capacity of entanglement as a natural diagnostic. The JT setting permits explicit saddle computations, adding a concrete data point to the literature on replica geometries and black-hole information.

major comments (1)

[§4 (late-time high-T regime) and the expansion around the factorized saddle] The large-c bath approximation is invoked to control the on-shell action in the late-time high-T regime. Because the capacity extracts the second derivative with respect to n (C ~ n² d²S_n/dn² at n=1), any n-dependent correction that is subleading for the first derivative can become leading for the second. The manuscript must supply an explicit error estimate or bound demonstrating that 1/c or fluctuation terms remain negligible at the order kept for the reported capacity correction; without this, the claim that the correction is definite is not yet secured.

minor comments (2)

[Introduction and §2] Notation for the replica parameter and the precise definition of the capacity (including the overall prefactor) should be stated once in a dedicated paragraph or equation to avoid ambiguity when comparing to the entropy.
[Abstract and §4] The abstract states a 'definite correction' without quoting the explicit formula; adding the leading expression for the capacity shift in the main text or a summary equation would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. The concern regarding the need for an explicit error estimate on subleading 1/c and fluctuation terms in the capacity calculation is well-taken, as the second n-derivative can amplify such contributions. We address this point below and will revise the manuscript to incorporate a dedicated error analysis in §4.

read point-by-point responses

Referee: [§4 (late-time high-T regime) and the expansion around the factorized saddle] The large-c bath approximation is invoked to control the on-shell action in the late-time high-T regime. Because the capacity extracts the second derivative with respect to n (C ~ n² d²S_n/dn² at n=1), any n-dependent correction that is subleading for the first derivative can become leading for the second. The manuscript must supply an explicit error estimate or bound demonstrating that 1/c or fluctuation terms remain negligible at the order kept for the reported capacity correction; without this, the claim that the correction is definite is not yet secured.

Authors: We agree that a rigorous bound is required to confirm that the reported O(1) correction to the capacity remains uncontaminated by subleading terms. In the revised version we will add an explicit error estimate in §4. The factorized saddle is controlled by the large-c limit, where the on-shell action receives Gaussian fluctuation corrections suppressed by 1/c. Because the leading correction to the capacity arises from the explicit n-dependence of the replica geometry (which enters at order 1 in the large-c expansion), the fluctuation contributions to the second n-derivative remain O(1/c) and are therefore negligible at the order kept in our calculation. This bound will be derived by expanding the replica action to quadratic order in fluctuations and differentiating twice with respect to n before taking the large-c limit. revision: yes

Circularity Check

0 steps flagged

No circularity: capacity correction follows from direct evaluation of replica saddle

full rationale

The derivation computes the capacity as the second n-derivative of the on-shell replica action in the factorized island saddle of JT gravity plus large-c bath. The late-time high-T expansion is performed explicitly on the n-dependent geometry; the entropy (first derivative) remains flat at the kept order while the second derivative acquires a nonzero term. This is a standard replica-trick calculation with an external large-c control parameter, not a self-definition, fitted input renamed as prediction, or load-bearing self-citation. The result is independent of the target observable and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the standard JT gravity plus large-c bath setup and the replica trick; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption JT gravity coupled to a large-c bath admits a controlled factorized island branch
Invoked to justify the semiclassical saddle used for both entropy and capacity.
standard math The replica trick and n to 1 limit can be extended to the capacity observable
Required to define the capacity from the replica partition function.

pith-pipeline@v0.9.0 · 5472 in / 1232 out tokens · 49759 ms · 2026-05-10T19:32:45.604773+00:00 · methodology

discussion (0)

Reference graph

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