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arxiv: 2309.04231 · v3 · submitted 2023-09-08 · ✦ hep-th

Subregion Complementarity in AdS/CFT

Sotaro Sugishita , Seiji Terashima This is my paper

Pith reviewed 2026-05-24 06:36 UTC · model grok-4.3

classification ✦ hep-th
keywords AdS/CFTbulk reconstructionentanglement wedgesubregion dualitysubregion complementaritylarge N limitblack hole horizons
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The pith

Subregion duality fails in AdS/CFT as causal wedge and global reconstructions disagree at leading large N order.

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

The paper examines bulk reconstruction in the AdS/CFT correspondence and shows that subregion duality does not hold. Discrepancies appear between operators obtained from causal wedge reconstruction and those from global reconstruction already at the leading order in the large N limit. The authors argue that this invalidates the entanglement wedge reconstruction proposal based on holographic quantum error correction codes, attributing the mismatch to non-perturbative finite N effects or quantum gravity effects from trans-Planckian modes near the horizon. They propose subregion complementarity instead, under which different CFT operators can describe the same bulk subregion. This complementarity is expected to hold outside the horizon for general eternal black holes but does not apply to single-sided black holes.

Core claim

The central claim is that subregion duality fails to hold because operators in causal wedge reconstruction differ from those in global reconstruction at leading order in the large N limit. This discrepancy shows the invalidity of entanglement wedge reconstruction based on the holographic quantum error correction code. The paper proposes subregion complementarity, in which different CFT operators can describe a bulk subregion, and states that this holds outside the horizon in general eternal black holes but is inapplicable for single-sided black holes where a semi-classical description at the stretched horizon is absent.

What carries the argument

Subregion complementarity, the proposal that different CFT operators can describe the same bulk subregion.

Load-bearing premise

Discrepancies between causal wedge and global reconstructions at leading order in large N indicate that entanglement wedge reconstruction is invalid.

What would settle it

An explicit large N calculation of a bulk operator reconstructed both from a subregion's causal wedge and from the global boundary that shows whether the two operators agree or disagree.

Figures

Figures reproduced from arXiv: 2309.04231 by Seiji Terashima, Sotaro Sugishita.

Figure 1
Figure 1. Figure 1: AdS-Rinlder subregion. In the left figure, [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
read the original abstract

We examine the bulk reconstruction in the AdS/CFT correspondence. We demonstrate that the subregion duality fails to hold, highlighting discrepancies between operators in causal wedge reconstruction and those in global reconstruction at the leading order in the large $N$ limit. We argue the invalidity of the entanglement wedge reconstruction based on the holographic quantum error correction code, attributing it to non-perturbative finite $N$ effects or quantum gravity effects due to the trans-Planckian modes near the horizon. Nevertheless, we propose the subregion complementarity, illustrating that different CFT operators can describe a bulk subregion. While we expect that this complementarity is valid outside the horizon in general eternal black holes, it is inapplicable for single-sided black holes where a semi-classical description at the stretched horizon is absent.

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 claims that subregion duality in AdS/CFT fails, as evidenced by discrepancies between causal-wedge and global reconstruction operators at leading order in the large-N limit. It argues that entanglement-wedge reconstruction is invalid due to non-perturbative finite-N effects or trans-Planckian modes near the horizon, and proposes 'subregion complementarity' in which different CFT operators can describe the same bulk subregion, valid for eternal black holes outside the horizon but not for single-sided black holes.

Significance. If the discrepancies at leading large N are shown to be robust and the complementarity proposal is derived without relying on the very framework it critiques, the work could challenge standard subregion duality and holographic quantum error correction in AdS/CFT. The paper offers a conceptual proposal rather than a fully derived result, with the large-N counting issue limiting its immediate implications.

major comments (1)
  1. [Abstract] Abstract: discrepancies between causal-wedge and global reconstruction are stated to appear at leading order in the large-N limit, yet the failure of entanglement-wedge reconstruction is attributed to non-perturbative finite-N effects or trans-Planckian modes. Leading order in 1/N is the strict N→∞ saddle where all 1/N corrections (perturbative and non-perturbative) vanish by definition; an effect visible at this order cannot be explained by finite-N corrections. This order-counting inconsistency is load-bearing for the central claim that subregion duality fails.
minor comments (1)
  1. The argument invokes the holographic quantum error correction code from prior literature; a self-contained derivation or explicit operator-level comparison at leading large N would strengthen the presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the important issue of large-N order counting. We address the major comment below and will make revisions to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: discrepancies between causal-wedge and global reconstruction are stated to appear at leading order in the large-N limit, yet the failure of entanglement-wedge reconstruction is attributed to non-perturbative finite-N effects or trans-Planckian modes. Leading order in 1/N is the strict N→∞ saddle where all 1/N corrections (perturbative and non-perturbative) vanish by definition; an effect visible at this order cannot be explained by finite-N corrections. This order-counting inconsistency is load-bearing for the central claim that subregion duality fails.

    Authors: We agree that the abstract as written creates an apparent inconsistency in the order counting that needs to be resolved. The discrepancies between causal-wedge and global reconstruction operators are computed explicitly at leading order in the large-N limit (i.e., they differ by O(1) terms, not suppressed by 1/N). The primary mechanism we invoke for why entanglement-wedge reconstruction fails is quantum-gravity effects from trans-Planckian modes near the horizon; these are not 1/N-suppressed and can invalidate the semi-classical assumptions underlying standard subregion duality even in the strict N→∞ limit. The reference to non-perturbative finite-N effects was intended as a secondary possibility and is not required for the leading-order claim. We will revise the abstract and the relevant discussion sections to emphasize the trans-Planckian mechanism as the leading explanation and to remove any ambiguity about order counting. This clarification does not change the central results but strengthens the presentation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The provided abstract and text excerpts show the paper demonstrating discrepancies at leading large-N order between causal-wedge and global reconstructions, then attributing entanglement-wedge issues to finite-N or trans-Planckian effects while proposing subregion complementarity. No quoted step reduces a claimed prediction or first-principles result to its own inputs by construction (self-definitional, fitted-input-as-prediction, or self-citation load-bearing). The reference to the holographic quantum error correction code draws on prior literature without evidence here of a self-referential chain where the central claim depends solely on unverified self-citation. The derivation chain is self-contained against external AdS/CFT benchmarks and does not exhibit the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The analysis rests on standard AdS/CFT assumptions and prior concepts like holographic QEC without new independent support provided in the abstract.

axioms (2)
  • domain assumption AdS/CFT correspondence holds and allows bulk reconstruction
    Entire analysis performed within AdS/CFT framework as stated in abstract.
  • domain assumption Large N limit captures leading order behavior for reconstruction
    Discrepancies identified specifically at leading order in large N.
invented entities (1)
  • subregion complementarity no independent evidence
    purpose: Alternative to subregion duality allowing multiple CFT operators for one bulk subregion
    New concept introduced to address the failure of standard duality.

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