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arxiv: 2606.12526 · v1 · pith:KFHL4G26new · submitted 2026-06-10 · ✦ hep-th · cond-mat.stat-mech· quant-ph

Multi-entropy in heavy local quenches

Kosei Fujiki , Kenya Tasuki This is my paper

Pith reviewed 2026-06-27 09:00 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechquant-ph
keywords multi-entropylocal quenchesholographic CFTgeodesic networkstripartite entanglementheavy operatorsvacuum block approximation
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The pith

In sharp heavy local quenches, genuine multi-entropy evolves as logarithms of rational time functions independent of heavy operator dimension.

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

The paper shows that for heavy local quenches in two-dimensional holographic conformal field theories, the genuine multi-entropy of adjacent intervals follows a specific time evolution fixed by kinematics. This evolution consists of logarithms of rational functions of time and does not depend on the dimension of the heavy operator. The result holds in both the bulk geodesic calculation with full backreaction and the boundary CFT computation using the heavy-light vacuum block approximation. A sympathetic reader would care because it implies that this measure of tripartite entanglement is set by the choice of global saddle points in the geometry rather than by details of local energy or particle propagation.

Core claim

In the sharp quench limit the time dependence of genuine multi-entropy is kinematically fixed to logarithms of rational functions of time and is independent of the heavy operator dimension. This arises in the bulk from a mismatch between the winding selected by the trivalent geodesic network and the windings selected independently by the pairwise geodesics in the fully back-reacted geometry. The CFT side reproduces the formula when the branch choice in the heavy-background uniformization map corresponds to the winding selection in the bulk.

What carries the argument

The vacuum-subtracted genuine multi-entropy computed from the mismatch in selected windings of the trivalent geodesic network versus pairwise geodesics.

If this is right

  • The first-order small-mass perturbation around the vacuum geodesic network cancels identically at any time after the quench.
  • The genuine multi-entropy is controlled by global saddle selection rather than local energy response or quasiparticle propagation.
  • The time dependence is the same in bulk and boundary calculations under the stated approximations.
  • Results apply specifically to tripartite entanglement of adjacent intervals in the sharp quench limit.

Where Pith is reading between the lines

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

  • If the winding mismatch mechanism generalizes, similar kinematic control might appear in other multi-partite entanglement measures in holographic setups.
  • Testing in non-holographic CFTs could reveal whether the independence from operator dimension requires holography.
  • The cancellation of perturbative corrections suggests robustness of the vacuum network at leading order.

Load-bearing premise

The branch choice in the heavy-background uniformization map corresponds exactly to the winding selection in the bulk geodesic network.

What would settle it

A computation of genuine multi-entropy in the same setup but using a different approximation or in a CFT without holographic dual that yields a different time dependence or dependence on operator dimension would falsify the claim.

read the original abstract

We study the time evolution of tripartite entanglement in heavy local quenches in two-dimensional holographic conformal field theories. Our diagnostic is the genuine multi-entropy of adjacent intervals, computed from both bulk and boundary perspectives. A perturbative bulk analysis shows that the first-order small-mass perturbation around the vacuum geodesic network cancels identically at any time after the quench. In the fully back-reacted geometry, a vacuum-subtracted genuine multi-entropy arises from a mismatch between the winding selected by the trivalent geodesic network and the windings selected independently by the pairwise geodesics. In the sharp quench limit, the time dependence of genuine multi-entropy is kinematically fixed to logarithms of rational functions of time and is independent of the heavy operator dimension. The CFT calculation reproduces the same formula within the heavy-light vacuum block approximation, where the branch choice in the heavy-background uniformization map corresponds to the winding selection in the bulk. These results indicate that, in this setup, the genuine multi-entropy is controlled by global saddle selection, rather than by a local energy response or quasiparticle propagation.

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 studies the time evolution of genuine tripartite multi-entropy for adjacent intervals following a heavy local quench in two-dimensional holographic CFTs. Bulk geodesic computations show that the first-order perturbative correction around the vacuum network cancels identically at all post-quench times; the vacuum-subtracted quantity in the fully back-reacted geometry arises from a mismatch between the winding selected by the trivalent network and those selected by the pairwise geodesics. In the sharp-quench limit this time dependence reduces to logarithms of rational functions of time and is independent of the heavy-operator dimension. The CFT computation reproduces the same expression within the heavy-light vacuum-block approximation, where the branch choice in the uniformization map is identified with the bulk winding selection. The authors conclude that genuine multi-entropy is controlled by global saddle selection rather than local energy response or quasiparticle propagation.

Significance. If the central identification holds, the result supplies a concrete example in which a higher-partite entanglement measure is fixed by global geometric data (saddle/winding selection) rather than by local dynamics, extending the kinematic understanding of holographic entanglement beyond the usual Ryu-Takayanagi formula. The explicit demonstration of perturbative cancellation and the parameter-free sharp-quench formula are concrete strengths.

major comments (2)
  1. [Abstract and CFT calculation] Abstract (final paragraph) and the corresponding CFT section: the statement that 'the branch choice in the heavy-background uniformization map corresponds to the winding selection in the bulk' is asserted without an explicit step-by-step matching between the selected uniformization branch and the mismatch that survives the first-order cancellation. Because this identification is load-bearing for the claim that the result is independent of the heavy-operator dimension and is controlled by global saddles rather than local response, a detailed derivation (including how the heavy-light block selects the relevant sheet) is required.
  2. [Bulk geodesic analysis] Bulk analysis (perturbative cancellation): while the abstract states that the first-order small-mass perturbation cancels identically, the manuscript does not supply the explicit expansion of the geodesic lengths or the error estimate that would confirm the cancellation persists beyond linear order in the regimes relevant to the sharp-quench limit.
minor comments (2)
  1. [Introduction] The definition of genuine multi-entropy (presumably Eq. (X) in the introduction) should be restated with explicit reference to the tripartite combination that subtracts the pairwise entropies, to avoid ambiguity when comparing bulk and CFT expressions.
  2. Notation for the heavy-operator dimension and the quench time should be unified between the bulk and CFT sections to facilitate direct comparison of the final formulas.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The two major comments identify areas where the presentation can be strengthened with additional explicit derivations. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and CFT calculation] Abstract (final paragraph) and the corresponding CFT section: the statement that 'the branch choice in the heavy-background uniformization map corresponds to the winding selection in the bulk' is asserted without an explicit step-by-step matching between the selected uniformization branch and the mismatch that survives the first-order cancellation. Because this identification is load-bearing for the claim that the result is independent of the heavy-operator dimension and is controlled by global saddles rather than local response, a detailed derivation (including how the heavy-light block selects the relevant sheet) is required.

    Authors: We agree that an explicit step-by-step matching between the uniformization branch and the bulk winding selection would make the central identification more transparent. In the revised manuscript we will insert a dedicated paragraph (or short subsection) in the CFT section that traces the heavy-light vacuum-block computation: starting from the uniformization map for the heavy background, identifying the branch points selected by the heavy-light OPE, showing how this branch choice reproduces the winding mismatch that survives the first-order bulk cancellation, and confirming that the resulting expression is independent of the heavy-operator dimension. This will directly support the claim that global saddle selection, rather than local response, controls the genuine multi-entropy. revision: yes

  2. Referee: [Bulk geodesic analysis] Bulk analysis (perturbative cancellation): while the abstract states that the first-order small-mass perturbation cancels identically, the manuscript does not supply the explicit expansion of the geodesic lengths or the error estimate that would confirm the cancellation persists beyond linear order in the regimes relevant to the sharp-quench limit.

    Authors: The manuscript establishes the identical first-order cancellation by showing that every linear correction to the individual geodesic lengths cancels when assembled into the trivalent network. To meet the request for explicit detail, the revised version will include the term-by-term expansion of the geodesic lengths in the small-mass limit (both for the pairwise geodesics and for the trivalent network) together with a short discussion of the error estimate. We will argue that, in the sharp-quench regime, higher-order terms remain sub-leading and do not modify the leading logarithmic time dependence fixed by the winding mismatch. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain.

full rationale

The paper derives the time dependence of genuine multi-entropy from a bulk analysis of geodesic winding mismatches in the fully back-reacted geometry after first-order cancellation, then states that the CFT heavy-light vacuum block reproduces the identical kinematic formula. The branch-winding correspondence is presented as an identification within the approximation setup rather than a self-referential definition or a parameter fitted to the target result. No self-citations, ansatzes smuggled via prior work, or reductions of the central prediction to its own inputs by construction appear in the abstract or described steps. The two routes are treated as independent and cross-checked.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the AdS/CFT dictionary for 2D CFTs and on the heavy-light vacuum block approximation; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The AdS/CFT correspondence equates bulk geodesic quantities with boundary entanglement measures for the CFTs under study.
    Invoked to translate bulk geodesic network results into CFT multi-entropy.

pith-pipeline@v0.9.1-grok · 5717 in / 1346 out tokens · 35452 ms · 2026-06-27T09:00:37.506928+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

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

  1. The Entanglement Wedge Polygon

    hep-th 2026-06 unverdicted novelty 6.0

    The paper defines the entanglement wedge polygon as the intersection of entanglement wedges external to individual homology regions and studies its topological and geometric properties in AdS examples.

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