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arxiv: 2604.03003 · v1 · submitted 2026-04-03 · ✦ hep-th · gr-qc

Black Hole Interior Operators and Dilatation Symmetry in Planar Black Branes

Nirmalya Kajuri This is my paper

Pith reviewed 2026-05-13 18:06 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords black hole interiorAdS black branesmirror operatorsdilatation symmetryscaling covariancebulk reconstructionstate-dependent operators
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The pith

Mirror operators for black hole interiors satisfy the dilatation covariance condition required by planar AdS black branes.

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

Planar AdS black branes possess a scaling symmetry that maps solutions at one temperature to solutions at another. Boundary representations of bulk interior modes are therefore expected to inherit this symmetry, meaning their correlators must transform covariantly under boundary dilatations. The paper derives the precise covariance condition that any such representation must obey. It then verifies that the state-dependent mirror operators introduced by Papadodimas and Raju satisfy the condition exactly. This establishes that the reconstruction of the black hole interior remains compatible with the brane's scaling symmetry.

Core claim

The Papadodimas-Raju mirror operators satisfy the covariance condition that any boundary representation of interior modes in a planar AdS black brane should satisfy, thereby inheriting the scaling symmetry of the planar black brane despite their state dependence.

What carries the argument

The covariance condition under boundary dilatations, which requires that correlators of interior-mode operators transform according to the scaling symmetry that maps the black brane at one temperature to another.

Load-bearing premise

Boundary representations of bulk interior modes must inherit the scaling symmetry of the planar black brane so that their correlators transform covariantly under dilatations.

What would settle it

An explicit computation of two-point functions of the mirror operators that fails to show the required covariance under a boundary dilatation transformation would falsify the central claim.

read the original abstract

Planar AdS black branes have a scaling symmetry that maps a brane solution at one temperature to a solution at another. It is natural to expect that boundary representations of bulk field modes should inherit this symmetry i.e. their correlators should transform covariantly under boundary dilatations. We derive a covariance condition that any boundary representation of interior modes in a planar AdS black brane should satisfy. We then show that Papadodimas-Raju mirror operators satisfy this condition. Thus the Papadodimas-Raju reconstruction of the bulk interior, although state-dependent, inherits the scaling symmetry of planar AdS black holes.

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 derives a covariance condition that any boundary representation of interior bulk modes in planar AdS black branes must satisfy, based on the scaling symmetry that maps black-brane solutions at one temperature to solutions at another temperature. It then performs an explicit check showing that the Papadodimas-Raju mirror operators obey this condition, thereby establishing that their state-dependent reconstruction inherits the dilatation symmetry of the planar black branes.

Significance. If the verification holds, the result supplies a non-trivial consistency check for state-dependent bulk reconstructions in the planar limit. It demonstrates that the mirror-operator construction respects a symmetry of the boundary theory without introducing additional parameters, which is relevant for ongoing discussions of black-hole interiors and the information paradox.

major comments (1)
  1. [Main text after covariance condition] The verification that the Papadodimas-Raju operators satisfy the covariance condition (main text, after Eq. (condition)): the substitution into the correlators must be shown in full detail so that it is clear the transformation reduces exactly to the required dilatation factor without relying on additional state-dependent adjustments not already present in the operator definition.
minor comments (1)
  1. [Section deriving covariance condition] Notation for the boundary dilatation generator and the explicit form of the two-point functions used in the check should be defined once at the beginning of the relevant section to improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the constructive suggestion for improving the clarity of the verification. We address the comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Main text after covariance condition] The verification that the Papadodimas-Raju operators satisfy the covariance condition (main text, after Eq. (condition)): the substitution into the correlators must be shown in full detail so that it is clear the transformation reduces exactly to the required dilatation factor without relying on additional state-dependent adjustments not already present in the operator definition.

    Authors: We agree that the verification step would benefit from expanded detail. In the revised manuscript we will add an explicit, step-by-step substitution of the Papadodimas-Raju mirror operators into the relevant boundary correlators immediately following Eq. (condition). The calculation will demonstrate that the dilatation transformation produces precisely the required scaling factor, relying solely on the state-dependent definition of the mirror operators and the known transformation properties of the boundary fields, without introducing any further state-dependent adjustments. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper first derives a covariance condition for boundary representations of interior modes by requiring that their correlators transform appropriately under dilatations induced by the planar black brane scaling symmetry (which maps solutions at different temperatures). It then performs an explicit verification that the independently constructed Papadodimas-Raju mirror operators satisfy this condition. This check does not reduce by the paper's own equations to a quantity already built into the operator definition or to a self-citation chain; the condition is motivated externally by bulk symmetry and the operators are taken from prior work without overlap in authorship. No load-bearing step collapses to a fit, renaming, or ansatz smuggled via self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the standard holographic dictionary relating bulk fields to boundary operators and on the known scaling symmetry of planar AdS black brane solutions; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Planar AdS black branes possess a scaling symmetry that maps a solution at one temperature to a solution at another temperature.
    Invoked in the first sentence of the abstract as the starting point for the covariance condition.
  • domain assumption Boundary representations of bulk modes must have correlators that transform covariantly under boundary dilatations.
    Stated as the natural expectation that motivates the covariance condition.

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discussion (0)

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Reference graph

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