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arxiv: 2606.00488 · v1 · pith:BVTLH7VDnew · submitted 2026-05-30 · ✦ hep-th · gr-qc

Massless Islands in Wedge Holography

Naman Kumar This is my paper

Pith reviewed 2026-06-28 18:41 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords wedge holographyentanglement islandsmassless gravitondefect CFTRyu-Takayanagi surfacegeneralized entropyquantum extremality
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The pith

A defect CFT at the wedge corner supplies an auxiliary entropy term that stabilizes massless islands without ghosts.

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

The paper shows that massless islands become possible in wedge holography once a unitary defect CFT is localized at the codimension-two corner. Its entropy, computed by an auxiliary bulk Ryu-Takayanagi surface, can vary opposite to the wedge area when the wedge endpoint fixes the defect region. This opposition balances the collapse to the horizon while all couplings and central charges stay positive. A local endpoint model produces an isolated stable saddle that dominates at late times. The result identifies the missing healthy entropy term, not masslessness, as the original obstruction.

Core claim

When the wedge endpoint position determines the defect entangling region, the auxiliary area can have the opposite variation to the wedge area while all couplings and central charges remain positive. The quantum extremality condition then replaces the pure orthogonality condition and allows a non-horizon island saddle in a long-range, massless, ghost-free gravitational theory.

What carries the argument

The auxiliary bulk Ryu-Takayanagi surface that computes the entropy of the additional defect CFT localized at the codimension-two corner.

If this is right

  • The quantum extremality condition replaces orthogonality and permits a non-horizon island saddle.
  • A local endpoint model exhibits an isolated stable saddle.
  • This saddle dominates over the Hartman-Maldacena surface at late times.
  • All couplings and central charges remain positive with no ghosts introduced.

Where Pith is reading between the lines

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

  • Corner-localized CFTs may supply balancing entropy terms in other brane or wedge setups with massless modes.
  • The same auxiliary-surface construction could be checked for stability when the defect is dynamical rather than fixed.
  • Explicit calculations in concrete defect CFTs would test whether the opposing variation holds beyond the local model.
  • The approach suggests examining whether similar corner sectors resolve island obstructions in non-holographic massless gravity models.

Load-bearing premise

The defect theory is holographic so its entropy is given by an auxiliary surface whose area variation opposes the wedge area when the wedge endpoint sets the defect region, while couplings and central charges stay positive.

What would settle it

An explicit computation of the auxiliary surface area as a function of the wedge endpoint in the local model, checking whether its variation opposes the wedge area and produces a stable saddle that dominates late times.

Figures

Figures reproduced from arXiv: 2606.00488 by Naman Kumar.

Figure 1
Figure 1. Figure 1: FIG. 1. The three equivalent descriptions in wedge hologra [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Defect-assisted wedge island. The wedge RT surface [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Entanglement islands are usually easiest to realize in doubly holographic models with massive gravitons or non-gravitating baths. In wedge holography, by contrast, Neumann boundary conditions on both branes give a normalizable massless graviton, but the island saddle of the purely geometric Ryu-Takayanagi problem collapses to the horizon. Negative Dvali-Gabadadze-Porrati (DGP) terms can restore nontrivial islands by changing the endpoint condition of the extremal surface, but this branch contains a massive ghost. We propose a different, manifestly healthy mechanism. We keep the wedge gravitational action free of DGP terms and add a unitary defect conformal field theory localized at the codimension-two corner. This sector is distinct from the standard corner CFT dual to the undeformed wedge, whose entropy is already represented by the wedge RT area; hence no double counting is involved. The entropy of this additional defect sector contributes to the generalized entropy. If the defect theory is holographic, this entropy is computed by an auxiliary bulk Ryu-Takayanagi surface. We show that when the wedge endpoint position determines the defect entangling region, the auxiliary area can have the opposite variation to the wedge area while all couplings and central charges remain positive. A local endpoint model exhibits an isolated stable saddle and its late-time dominance over the Hartman-Maldacena surface. The quantum extremality condition then replaces the pure orthogonality condition and allows a non-horizon island saddle in a long-range, massless, ghost-free gravitational theory. This demonstrates that the obstruction to massless islands in minimal wedge holography is not masslessness itself, but the absence of an additional healthy entropy term capable of balancing the horizon-minimizing area variation.

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

1 major / 1 minor

Summary. The manuscript proposes realizing entanglement islands in wedge holography with a massless graviton by introducing an additional unitary defect CFT localized at the codimension-two corner, distinct from the standard corner CFT. The entropy of this defect sector is computed via an auxiliary holographic RT surface; when the wedge endpoint determines the defect entangling region, the auxiliary area variation opposes the wedge area while couplings and central charges remain positive. This replaces the orthogonality condition with quantum extremality, yielding a stable non-horizon island saddle that dominates at late times over the Hartman-Maldacena surface in a ghost-free theory.

Significance. If the explicit calculations confirm the opposite variation and stable saddle, the result would demonstrate that massless islands are possible in healthy long-range gravity by supplying an additional balancing entropy term, rather than requiring massive gravitons or DGP terms. This addresses a key obstruction in minimal wedge holography and provides a concrete, falsifiable construction using a holographic defect sector.

major comments (1)
  1. [Abstract and local endpoint model] Abstract and the section describing the local endpoint model: the central claim that the auxiliary area has opposite variation to the wedge area (while keeping all couplings and central charges positive) is load-bearing for the proposal, yet the provided description states the result without explicit computation of the variations, the endpoint mapping, or the resulting quantum extremality condition; the manuscript must supply these derivations to substantiate the claim.
minor comments (1)
  1. Clarify with a diagram or explicit notation how the auxiliary bulk for the defect CFT is embedded relative to the wedge without introducing new gravitational degrees of freedom.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and for highlighting the need for explicit derivations to support the central claim. We agree that the manuscript requires additional calculations to substantiate the opposite variation of the auxiliary area and the resulting quantum extremality condition. We will revise the paper to include these derivations in the local endpoint model section.

read point-by-point responses

  1. Referee: [Abstract and local endpoint model] Abstract and the section describing the local endpoint model: the central claim that the auxiliary area has opposite variation to the wedge area (while keeping all couplings and central charges positive) is load-bearing for the proposal, yet the provided description states the result without explicit computation of the variations, the endpoint mapping, or the resulting quantum extremality condition; the manuscript must supply these derivations to substantiate the claim.

    Authors: We agree that the load-bearing claim requires explicit support. In the revised manuscript we will add the full computation of the auxiliary-area and wedge-area variations with respect to the endpoint position, the explicit mapping between the wedge endpoint and the defect entangling region, and the derivation of the quantum extremality condition that replaces the orthogonality condition. These additions will be placed in the local endpoint model section (and referenced from the abstract) while preserving the positivity of all couplings and central charges. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents an explicit model construction: a defect CFT is added at the codimension-two corner, its entropy is computed by the standard (externally grounded) holographic RT prescription, and a specific endpoint-to-entangling-region mapping is chosen so that the auxiliary area variation opposes the wedge area while keeping couplings positive. This is a model-building demonstration that an additional healthy entropy term can balance the variation, not a derivation in which a claimed prediction or first-principles result reduces by construction to the inputs. No self-citations, uniqueness theorems, fitted parameters renamed as predictions, or smuggled ansatze appear in the load-bearing steps. The auxiliary RT surface and quantum extremality condition are independent of the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard Ryu-Takayanagi prescription applied to both the wedge and an auxiliary surface, plus the domain assumption that the added defect CFT is unitary and distinct; a new entity (the defect sector) is introduced without independent evidence outside the model.

axioms (2)
  • standard math Ryu-Takayanagi formula computes holographic entanglement entropy for both the wedge and auxiliary surfaces
    Invoked for the main wedge area and the defect entropy contribution.
  • domain assumption The defect CFT is unitary and distinct from the standard corner CFT
    Required to ensure no double counting and to keep the theory healthy.
invented entities (1)
  • Additional unitary defect CFT sector localized at the codimension-two corner no independent evidence
    purpose: Supplies an extra entropy term in the generalized entropy that can balance the horizon-minimizing variation of the wedge area
    New sector introduced to solve the island problem without ghosts or DGP terms.

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Reference graph

Works this paper leans on

24 extracted references · 22 canonical work pages · 11 internal anchors

  1. [1]

    Entanglement Wedge Reconstruction and the Information Paradox

    G. Penington, Entanglement wedge reconstruction and the information paradox, JHEP09, 002 (2020), arXiv:1905.08255

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  2. [2]

    The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

    A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedgeofanevaporatingblackhole, JHEP12, 063(2019), arXiv:1905.08762

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  3. [3]

    The Page curve of Hawking radiation from semiclassical geometry

    A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP03, 149 (2020), arXiv:1908.10996

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  4. [4]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys.93, 035002 (2021), arXiv:2006.06872

    work page arXiv 2021

  5. [5]

    Locally Localized Gravity

    A. Karch and L.Randall, Locally localized gravity, JHEP 05, 008 (2001), arXiv:hep-th/0011156

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  6. [6]

    Holographic Dual of BCFT

    T. Takayanagi, Holographic dual of BCFT, Phys. Rev. Lett.107, 101602 (2011), arXiv:1105.5165

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  7. [7]

    Almheiri, R

    A. Almheiri, R. Mahajan, and J. E. Santos, Entangle- ment islands in higher dimensions, SciPost Phys.9, 001 (2020), arXiv:1911.09666

    work page arXiv 2020

  8. [8]

    Geng and A

    H. Geng and A. Karch, Massive islands, JHEP09, 121 (2020), arXiv:2006.02438

    work page arXiv 2020

  9. [9]

    I. Akal, Y. Kusuki, T. Takayanagi, and Z. Wei, Codi- mension two holography for wedges, Phys. Rev. D102, 126007 (2020), arXiv:2007.06800

    work page arXiv 2020

  10. [10]

    Hu and R.-X

    P.-J. Hu and R.-X. Miao, Effective action, spectrum and first law of wedge holography, JHEP03, 145 (2022), arXiv:2201.02014

    work page arXiv 2022

  11. [11]

    J. M. Maldacena, The LargeNlimit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231–252 (1998), arXiv:hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  12. [12]

    Witten, Anti de Sitter space and holography, Adv

    E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys.2, 253–291 (1998), arXiv:hep- th/9802150

    work page arXiv 1998

  13. [13]

    H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, and S. Shashi, Information transfer with a gravitating bath, SciPost Phys.10, 103 (2021), arXiv:2012.04671

    work page arXiv 2021

  14. [14]

    H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Ran- dall, M. Riojas, and S. Shashi, Inconsistency of islands in theories with long-range gravity, JHEP01, 182 (2022), arXiv:2107.03390

    work page arXiv 2022

  15. [15]

    G. R. Dvali, G. Gabadadze, and M. Porrati, 4D gravity on a brane in 5D Minkowski space, Phys. Lett. B485, 208 (2000), arXiv:hep-th/0005016

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  16. [16]

    Miao, Entanglement Island versus Massless Grav- ity, Eur

    R.-X. Miao, Entanglement Island versus Massless Grav- ity, Eur. Phys. J. C84, 123 (2024), arXiv:2212.07645

    work page arXiv 2024

  17. [17]

    Miao, Entanglement Island and Page Curve in Wedge Holography, JHEP03, 214 (2023), arXiv:2301.06285

    R.-X. Miao, Entanglement Island and Page Curve in Wedge Holography, JHEP03, 214 (2023), arXiv:2301.06285

    work page arXiv 2023

  18. [18]

    Holographic Derivation of Entanglement Entropy from AdS/CFT

    S. Ryu and T. Takayanagi, Holographic derivation of en- tanglement entropy from AdS/CFT, Phys. Rev. Lett.96, 181602 (2006), arXiv:hep-th/0603001

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  19. [19]

    R.Jackiw, Lowerdimensionalgravity, Nucl.Phys.B252, 343 (1985)

    1985

  20. [20]

    Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys

    C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B126, 41 (1983)

    1983

  21. [21]

    V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP07, 062 (2007), arXiv:0705.0016

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  22. [22]

    H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Ran- dall, M. Riojas, and S. Shashi, Jackiw–Teitelboim Grav- ityfromtheKarch–RandallBraneworld, Phys.Rev.Lett. 129, 231601 (2022), arXiv:2206.04695

    work page arXiv 2022

  23. [23]

    A. C. Wall, Maximin surfaces, and the strong subaddi- tivity of the covariant holographic entanglement entropy, Class. Quant. Grav.31, 225007 (2014), arXiv:1211.3494

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  24. [24]

    Time Evolution of Entanglement Entropy from Black Hole Interiors

    T. Hartman and J. Maldacena, Time Evolution of En- tanglement Entropy from Black Hole Interiors, JHEP05, 014 (2013), arXiv:1303.1080

    work page internal anchor Pith review Pith/arXiv arXiv 2013