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arxiv: 2604.27425 · v1 · submitted 2026-04-30 · ✦ hep-th

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Bulk Reconstruction in Bilocal Holography

Robert de Mello Koch , Animik Ghosh , Minkyoo Kim , Anik Rudra
Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:33 UTC · model grok-4.3

classification ✦ hep-th
keywords bilocal holographybulk reconstructionhigher-spin gravityvector-model CFTsubregion dualitygauge-fixed variablesAdS/CFT
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The pith

Bilocal holography yields a local bulk reconstruction formula that matches standard methods after data identification.

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

The paper establishes a bulk reconstruction procedure inside bilocal holography, a gauge-fixed framework for the higher-spin gravity dual to vector-model CFTs that works entirely with physical degrees of freedom. It produces a local formula for the bulk fields and verifies that this formula reproduces the standard reconstruction result once the same boundary data and gauge-fixed variables are used in both approaches. The work also shows how subregion duality arises by restricting the bilocal operators appropriately. A sympathetic reader cares because the method removes gauge ambiguities and offers a direct, constructive route from boundary data to bulk fields in these dualities.

Core claim

Bilocal holography supplies a remarkably local bulk reconstruction formula. When the same boundary data and gauge-fixed variables are identified as in conventional approaches, the formula agrees with standard bulk reconstruction. Subregion duality is realized in the framework by suitable restrictions on the bilocal operators.

What carries the argument

The bilocal field operators that encode the higher-spin gravity degrees of freedom in a completely gauge-fixed manner.

Load-bearing premise

The bilocal holography framework is a valid and complete gauge-fixed description of the higher-spin gravity dual, and the identification of boundary data and gauge-fixed variables with standard methods introduces no hidden assumptions.

What would settle it

A concrete calculation in a solvable higher-spin theory where the derived local formula produces a different bulk field value than the standard reconstruction for the exact same boundary data and gauge choice would show the claimed agreement fails.

read the original abstract

Bilocal holography provides a constructive approach to the higher-spin gravity theories dual to vector-model conformal field theories. Its central advantage is that it is completely gauge fixed and formulated entirely in terms of physical degrees of freedom. We derive a remarkably local bulk reconstruction formula and demonstrate its agreement with standard bulk reconstruction, after the same boundary data and gauge-fixed variables have been identified. We further clarify how subregion duality is realized in this framework.

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 derives a local bulk reconstruction formula within the bilocal holography framework, a completely gauge-fixed formulation of higher-spin gravity dual to vector-model CFTs. It demonstrates agreement with standard (HKLL-style) bulk reconstruction after the same boundary data and gauge-fixed variables are identified, and clarifies the realization of subregion duality.

Significance. If the identification step is shown to be unique and independent, the result would provide a constructive, physical-degree-of-freedom approach to bulk reconstruction in higher-spin theories, strengthening the case for locality in this setting and offering a concrete realization of subregion duality. The gauge-fixed nature is a genuine advantage over standard formulations.

major comments (2)
  1. [Comparison with standard reconstruction] The agreement with standard reconstruction is stated to hold only after identification of boundary data and gauge-fixed variables (abstract and the comparison section). The manuscript must explicitly demonstrate that this identification is unique, information-preserving, and does not rely on prior knowledge of the bulk-boundary dictionary or additional constraints not already present in the bilocal setup; otherwise the locality claim risks being tautological rather than derived.
  2. [Derivation of the reconstruction formula] The derivation of the bulk reconstruction formula (the section presenting the local formula) should include an explicit check that no higher-spin constraints or gauge redundancies from the vector-model dual are discarded during the variable identification, as this would affect whether the formula is truly independent.
minor comments (2)
  1. Clarify the notation for bilocal fields versus standard bulk fields to avoid ambiguity when comparing the two reconstructions.
  2. [Subregion duality discussion] Add a brief remark on how the subregion duality clarification connects to existing literature on entanglement wedges in higher-spin theories.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comments. These points help clarify the presentation of the identification between bilocal variables and standard boundary data. We address each comment below and will incorporate the requested clarifications into a revised version of the manuscript.

read point-by-point responses

  1. Referee: [Comparison with standard reconstruction] The agreement with standard reconstruction is stated to hold only after identification of boundary data and gauge-fixed variables (abstract and the comparison section). The manuscript must explicitly demonstrate that this identification is unique, information-preserving, and does not rely on prior knowledge of the bulk-boundary dictionary or additional constraints not already present in the bilocal setup; otherwise the locality claim risks being tautological rather than derived.

    Authors: We agree that an explicit demonstration of uniqueness and information preservation strengthens the result. In the bilocal framework the identification is constructed directly from the CFT two-point functions and the definition of the bilocal fields as physical degrees of freedom; it does not presuppose the full bulk-boundary dictionary. In the revised manuscript we will add a dedicated subsection that (i) writes the explicit one-to-one map between the bilocal bilocal operator and the gauge-fixed higher-spin boundary values, (ii) verifies that the map is invertible by reconstructing the bilocal correlators from the identified data, and (iii) shows that no external bulk knowledge is used beyond the standard CFT-to-bulk matching of two-point functions already present in the bilocal setup. This makes the locality of the reconstruction formula a derived property of the bilocal equations rather than an assumption. revision: yes

  2. Referee: [Derivation of the reconstruction formula] The derivation of the bulk reconstruction formula (the section presenting the local formula) should include an explicit check that no higher-spin constraints or gauge redundancies from the vector-model dual are discarded during the variable identification, as this would affect whether the formula is truly independent.

    Authors: We concur that such a check is necessary for independence. Because bilocal holography is formulated entirely in terms of gauge-fixed physical degrees of freedom, the higher-spin constraints (tracelessness, conservation, and the appropriate Ward identities) are already encoded in the bilocal field definitions and are preserved verbatim under the identification. In the revised manuscript we will insert an explicit verification paragraph (and, if space permits, a short appendix) that tracks each constraint through the variable map and confirms none are lost or imposed by hand. This establishes that the local reconstruction formula is obtained strictly within the bilocal framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper derives a local bulk reconstruction formula within the bilocal holography framework and demonstrates agreement with standard reconstruction after identifying matching boundary data and gauge-fixed variables. No equations, self-citations, or parameter fits are quoted that reduce the derived formula to the inputs by construction. The identification step serves as a comparison between frameworks rather than embedding the target result into the derivation itself. The bilocal approach is presented as a self-contained, gauge-fixed construction in terms of physical degrees of freedom, making the overall chain independent of the standard HKLL-style result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The work rests on the standard AdS/CFT correspondence for vector models and higher-spin gravity.

axioms (1)
  • domain assumption The AdS/CFT correspondence holds for vector-model CFTs and their higher-spin gravity duals.
    This is the foundational assumption enabling bilocal holography as a constructive approach.

pith-pipeline@v0.9.0 · 5362 in / 1414 out tokens · 85918 ms · 2026-05-07T08:33:12.381246+00:00 · methodology

discussion (0)

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Reference graph

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