arxiv: 2604.18405 · v1 · submitted 2026-04-20 · ✦ hep-th

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Large-c BCFT Entanglement Entropy with Deformed Boundaries from Emergent JT Gravity

Dominik Neuenfeld , Christopher Tellinger

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:52 UTC · model grok-4.3

classification ✦ hep-th

keywords BCFTentanglement entropyJT gravityisland formulaboundary deformationslarge central chargevon Neumann entropyAdS2

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The pith

At large central charge, von Neumann entropy in a BCFT with deformed boundaries equals the island entropy of the same interval in an undeformed BCFT coupled to JT gravity.

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

The paper examines how small deformations of the boundary in two-dimensional boundary conformal field theories change the entanglement entropy of intervals, both at zero and finite temperature. These deformations are infinitesimal conformal transformations that shift the boundary location and can be treated as perturbations involving the boundary displacement operator. At large central charge, the resulting entropy is shown to match exactly the island entropy computed in an undeformed copy of the same BCFT that serves as a bath and is joined to an AdS2 region governed by Jackiw-Teitelboim gravity. The deformation enters the gravitational side solely through the boundary condition imposed on the dilaton field, while transparent boundary conditions connect the two sides. This matching holds under assumptions on the BCFT spectrum and operator product coefficients that permit an exponentially large number of light operators.

Core claim

We demonstrate that at large central charge the von Neumann entropy in the presence of a deformed boundary is reproduced by the island entropy of the same interval in an undeformed BCFT acting as a bath and coupled to a gravitating spacetime. Here, the BCFT is joined to an AdS2 region governed by Jackiw-Teitelboim (JT) gravity via transparent boundary conditions. The boundary condition for the dilaton field is set by the boundary deformation in the BCFT computation. Our analysis relies on mild assumptions about the spectrum and OPE coefficients of the BCFT.

What carries the argument

Island entropy in an undeformed BCFT bath joined to JT gravity on AdS2, with the dilaton boundary condition fixed by the BCFT boundary deformation.

Load-bearing premise

The BCFT spectrum and OPE coefficients permit an exponentially large number of light operators.

What would settle it

Compute the von Neumann entropy directly in a solvable large-c BCFT with an explicit infinitesimal boundary deformation and check whether it equals the island entropy obtained from the corresponding JT gravity setup with the matching dilaton boundary condition.

read the original abstract

We study the effect of boundary deformations on the von Neumann entropy of subregions in two-dimensional boundary conformal field theories (BCFTs) at zero and finite temperature. The deformations considered are infinitesimal global conformal transformations that move the boundary and can equivalently be viewed as the leading-order effect of certain BCFT perturbations with the boundary displacement operator. We demonstrate that at large central charge the von Neumann entropy in the presence of a deformed boundary is reproduced by the island entropy of the same interval in an undeformed BCFT acting as a bath and coupled to a gravitating spacetime. Here, the BCFT is joined to an AdS$_2$ region governed by Jackiw-Teitelboim (JT) gravity via transparent boundary conditions. The boundary condition for the dilaton field is set by the boundary deformation in the BCFT computation. Our analysis relies on mild assumptions about the spectrum and OPE coefficients of the BCFT. Notably, these conditions are consistent with an exponentially large number of light operators and are therefore weaker than those required for holographic BCFTs. This is possible since the BCFT result is not reproduced by a gravitational computation in three dimensions with an O(1) number of matter fields, but instead by a computation in two dimensions and with an O(c) number of light fields.

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

This paper shows a clean leading-order match between deformed-boundary BCFT entropy and JT island entropy at large c, with the deformation entering only through the dilaton boundary condition.

read the letter

The main point is that at large central charge the von Neumann entropy of an interval in a BCFT with an infinitesimal boundary deformation is reproduced by the island entropy of the same interval in an undeformed BCFT bath coupled to JT gravity. The deformation is encoded solely in the dilaton boundary condition under transparent interface conditions, and the calculation covers both zero and finite temperature. This is done with O(c) light fields rather than the stricter O(1) matter setup of usual holographic BCFTs, which makes the assumptions weaker than standard holographic ones. The result is new in the sense that prior JT island literature did not explicitly treat boundary deformations this way. The paper does a solid job laying out the matching at leading order in the deformation and keeping the logic transparent once the spectrum assumptions are accepted. The assumptions themselves are stated plainly as mild and consistent with exponentially many light operators, which is a reasonable way to flag the scope without overclaiming. The soft spot is that those spectrum and OPE conditions are not derived in detail here, so it is hard to judge how much they constrain the result or whether they introduce any hidden selection. Because the deformations are infinitesimal, the work also leaves higher-order corrections untouched, which is acceptable for a first demonstration but narrows the immediate applicability. The citation pattern is standard and draws on the expected JT and BCFT entanglement references without obvious gaps. This paper is for people working on 2D gravity models, island formulas, and controlled large-c limits of boundary theories. A reader already familiar with JT gravity and holographic entanglement will get the most out of it and can assess the assumptions themselves. It deserves a serious referee because the matching is explicit and the setup is controlled enough to be worth checking, even if the spectrum assumptions will need scrutiny in review.

Referee Report

1 major / 2 minor

Summary. The paper claims that at large central charge, the von Neumann entropy of subregions in 2D BCFTs with infinitesimal boundary deformations (via global conformal maps or the boundary displacement operator) is exactly reproduced by the island entropy of the same interval in an undeformed BCFT bath coupled to JT gravity in AdS2, with the deformation entering solely through the dilaton boundary condition under transparent interface conditions. The reproduction holds under mild assumptions on the BCFT spectrum and OPE coefficients that permit an exponentially large number of light operators (weaker than holographic BCFT requirements) and is performed in a 2D gravity setup with O(c) light fields.

Significance. If the central reproduction holds, the result supplies a concrete gravitational dual for boundary-deformation effects on BCFT entanglement entropy via emergent JT gravity and the island formula. It is noteworthy for achieving the match with weaker spectrum assumptions than standard holographic BCFTs and for operating in two-dimensional gravity with parametrically many light fields rather than three-dimensional gravity with O(1) matter.

major comments (1)

[Abstract and main entropy derivation] The reproduction of the BCFT entropy by the island formula rests on unspecified 'mild assumptions about the spectrum and OPE coefficients' (stated in the abstract and used throughout the derivation). Without an explicit list of these assumptions together with a verification that they are satisfied by the operators contributing at leading order in 1/c, it is impossible to confirm that the match is free of hidden parameter dependence or post-hoc adjustments. This is load-bearing for the central claim.

minor comments (2)

The notation for the deformed boundary condition and its mapping to the dilaton boundary value should be cross-referenced explicitly between the BCFT and gravity sides to improve readability.
A brief remark on the range of validity of the infinitesimal-deformation approximation (e.g., relative to the interval size or temperature) would help readers assess the regime of applicability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recommending minor revision. We address the single major comment below and will incorporate the requested clarifications.

read point-by-point responses

Referee: [Abstract and main entropy derivation] The reproduction of the BCFT entropy by the island formula rests on unspecified 'mild assumptions about the spectrum and OPE coefficients' (stated in the abstract and used throughout the derivation). Without an explicit list of these assumptions together with a verification that they are satisfied by the operators contributing at leading order in 1/c, it is impossible to confirm that the match is free of hidden parameter dependence or post-hoc adjustments. This is load-bearing for the central claim.

Authors: We agree that an explicit enumeration of the assumptions, together with a verification that they hold for the operators that contribute at leading order in 1/c, will strengthen the presentation and remove any ambiguity. In the revised manuscript we will add a dedicated subsection (placed after the statement of the main result) that lists the assumptions in precise form: (i) the BCFT spectrum contains an exponentially large number of operators with conformal dimensions O(1) in the large-c limit; (ii) the OPE coefficients involving these light operators satisfy the standard large-c factorization and do not receive 1/c corrections that would alter the leading entropy; (iii) heavy operators (dimension ≫1) contribute only at sub-leading order in the replica-trick computation of the entropy. We will then verify, using the explicit form of the boundary deformation and the transparent-interface matching, that only the light operators enter the leading 1/c term of the island entropy. These conditions are already implicit in the derivation but were not collected in one place; the revision will make them manifest without introducing new parameter dependence or post-hoc adjustments. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes the large-c BCFT von Neumann entropy for an interval with infinitesimal boundary deformation (via global conformal maps or displacement operator) and shows it equals the island entropy of the same interval in an undeformed BCFT bath coupled to JT gravity, with the deformation entering only through the dilaton boundary condition under transparent interface conditions. This match is derived under explicitly stated mild spectrum and OPE assumptions that permit exponentially many light operators. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation chain; the gravity-side computation is presented as an independent emergent description rather than a renaming or tautological reproduction of the BCFT input. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on mild assumptions about the BCFT spectrum and OPE coefficients that permit an exponentially large number of light operators; these are domain assumptions rather than derived quantities.

axioms (1)

domain assumption Mild assumptions about the spectrum and OPE coefficients of the BCFT consistent with exponentially many light operators
Explicitly invoked in the abstract as the basis for the large-c demonstration.

pith-pipeline@v0.9.0 · 5528 in / 1316 out tokens · 31719 ms · 2026-05-10T04:52:49.792581+00:00 · methodology

discussion (0)

Reference graph

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