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arxiv: 2606.03106 · v1 · pith:Y3TICMBXnew · submitted 2026-06-02 · ✦ hep-th

Holographic reconstruction for defect CFTs from AdS_p times S^q spacetimes

Federico Faedo , Nicol\`o Petri , Alessia Segati This is my paper

Pith reviewed 2026-06-28 09:14 UTC · model grok-4.3

classification ✦ hep-th
keywords holographic renormalizationdefect CFTAdS x S geometriesRomans supergravityone-point correlatorsholographic stress tensorWard identities
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The pith

Holographic renormalization on fibered AdS_p × S^q spacetimes produces one-point correlators and the stress tensor for defect CFTs.

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

The paper shows how to apply holographic renormalization to AdS_p × S^q geometries fibered over an interval and coupled to gauge and scalar fields. A coordinate choice is identified that makes the boundary asymptotically flat, allowing standard counterterms to extract the one-point functions of bulk fields, the holographic stress tensor, and the associated Ward identities. The method is carried out in detail for line and surface defects in five- and six-dimensional Romans supergravity, with the resulting geometries preserving four supercharges and asymptoting to AdS5 or AdS6. These observables are then compared with expectations from the dual defect conformal field theory.

Core claim

By selecting coordinates on the fibered AdS_p × S^q spacetimes that admit an asymptotically flat boundary, holographic renormalization yields the one-point correlators of the bulk fields, the holographic stress tensor, and its Ward identities for the defect theory; the procedure is implemented explicitly for AdS2 × S2, AdS2 × S3, and AdS3 × S2 backgrounds in Romans supergravity.

What carries the argument

Fibered AdS_p × S^q geometries with higher-form gauge fields and scalars, renormalized via the standard procedure in asymptotically flat boundary coordinates.

If this is right

  • One-point correlators of the bulk fields are obtained for the defect theories.
  • The holographic stress tensor obeys Ward identities consistent with the presence of the defect.
  • Explicit results follow for line defects in five-dimensional and surface defects in six-dimensional Romans supergravity.
  • The observables can be compared directly with existing calculations in the defect CFT literature.

Where Pith is reading between the lines

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

  • The same coordinate and renormalization steps could be tested on other warped supergravity solutions containing defects.
  • If the method extends, it would supply a uniform way to read off defect data from any AdS_p × S^q fibration that reaches a flat boundary.
  • The resulting stress-tensor expressions might be used to constrain possible higher-order corrections in the supergravity action.

Load-bearing premise

The chosen coordinate system on the fibered geometries admits an asymptotically flat boundary that permits standard holographic renormalization without extra counterterms or obstructions.

What would settle it

An explicit computation of the holographic stress tensor components that fails to satisfy the expected Ward identities of the defect CFT would show the renormalization procedure does not apply as claimed.

read the original abstract

We study defects in superconformal field theories using holography, focusing on the precise derivation of the defect observables from supergravity. We consider $\mathrm{AdS}_p \times S^q$ spacetimes fibered over an interval and coupled to higher-form gauge fields as well as scalar fields. We determine the coordinate system in which the defect geometry admits an asymptotically flat boundary and, in this setup, we systematically apply holographic renormalization to compute the fundamental observables of the defect theory. In particular, we derive the one-point correlators of the bulk fields, the holographic stress tensor, and its Ward identities. We implement explicitly this procedure for line and surface defects in five- and six-dimensional Romans supergravity. The relevant geometries are $\mathrm{AdS}_2\times S^2$, $\mathrm{AdS}_2\times S^3$ and $\mathrm{AdS}_3\times S^2$ backgrounds warped over an interval, preserving four supercharges and asymptotically $\mathrm{AdS}_5$ and $\mathrm{AdS}_6$. In each case, we discuss the implications of our results and compare them with the standard literature on defects in conformal field theory.

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 / 1 minor

Summary. The paper claims to develop a holographic renormalization procedure for defect CFTs realized by AdS_p × S^q geometries fibered over an interval in Romans supergravity. It identifies a coordinate system yielding an asymptotically flat boundary, then applies standard holographic renormalization to derive one-point correlators of bulk fields, the holographic stress tensor, and its Ward identities. The procedure is implemented explicitly for line and surface defects corresponding to AdS2×S2, AdS2×S3, and AdS3×S2 backgrounds in five- and six-dimensional cases, with comparisons to existing defect CFT literature.

Significance. If the central derivations hold without hidden counterterms or coordinate obstructions, the work would supply explicit, computable expressions for defect observables in a class of supergravity backgrounds, enabling direct tests against field-theory expectations for one-point functions and stress-tensor Ward identities. This would strengthen the dictionary between holographic defect geometries and defect CFT data.

major comments (2)
  1. [Abstract and coordinate system discussion] Abstract (coordinate system and renormalization procedure): The central claim that the fibered AdS_p × S^q geometries admit an asymptotically flat boundary permitting standard holographic renormalization without additional counterterms is load-bearing for all subsequent derivations of the stress tensor and Ward identities. The manuscript must explicitly verify that the chosen radial coordinate and warping functions eliminate all divergent terms in the on-shell action at the orders relevant to the one-point function of the stress tensor; otherwise the Ward identities derived from it are not guaranteed to hold.
  2. [Implementation for Romans supergravity backgrounds] Implementation sections for AdS2×S2, AdS2×S3, AdS3×S2: The abstract states that the procedure is applied systematically, yet no explicit formulas, counterterm coefficients, or on-shell action expansions are referenced. Without these, it is impossible to confirm that the reported one-point correlators and stress-tensor components are independent of post-hoc choices rather than fixed by finiteness requirements.
minor comments (1)
  1. [Abstract] The abstract mentions preservation of four supercharges and asymptotic AdS5/AdS6; the manuscript should clarify whether supersymmetry is used to constrain the counterterms or only to select the backgrounds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments highlight the need for greater explicitness in verifying the renormalization procedure and in referencing the derived expressions. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and coordinate system discussion] Abstract (coordinate system and renormalization procedure): The central claim that the fibered AdS_p × S^q geometries admit an asymptotically flat boundary permitting standard holographic renormalization without additional counterterms is load-bearing for all subsequent derivations of the stress tensor and Ward identities. The manuscript must explicitly verify that the chosen radial coordinate and warping functions eliminate all divergent terms in the on-shell action at the orders relevant to the one-point function of the stress tensor; otherwise the Ward identities derived from it are not guaranteed to hold.

    Authors: We agree that an explicit verification of the cancellation of divergences is necessary to make the procedure fully rigorous. In the revised version we will insert a short dedicated subsection (or expanded paragraph) immediately after the coordinate-system discussion. This subsection will expand the on-shell action in the chosen radial coordinate, display the leading divergent terms order by order, and show that they are precisely canceled by the counterterms fixed by the warping functions, leaving only finite contributions at the orders relevant for the stress-tensor one-point function. This addition will confirm that no hidden counterterms are required. revision: yes

  2. Referee: [Implementation for Romans supergravity backgrounds] Implementation sections for AdS2×S2, AdS2×S3, AdS3×S2: The abstract states that the procedure is applied systematically, yet no explicit formulas, counterterm coefficients, or on-shell action expansions are referenced. Without these, it is impossible to confirm that the reported one-point correlators and stress-tensor components are independent of post-hoc choices rather than fixed by finiteness requirements.

    Authors: The explicit expressions for the counterterm coefficients (determined by requiring finiteness of the on-shell action), the renormalized one-point functions, and the stress-tensor components are already derived and written out in Sections 3–5 for each background. To make these results immediately locatable we will (i) add a sentence in the abstract and introduction that points to the relevant equations and (ii) include a short table summarizing the counterterm coefficients and the resulting finite stress-tensor components for the three cases. These changes will clarify that the expressions are fixed by the renormalization procedure rather than chosen ad hoc. revision: partial

Circularity Check

0 steps flagged

No significant circularity in holographic renormalization derivation

full rationale

The paper determines a coordinate system on fibered AdS_p × S^q geometries that admits an asymptotically flat boundary, then applies standard holographic renormalization to derive one-point correlators, the holographic stress tensor, and Ward identities from the supergravity action for specific Romans backgrounds. No load-bearing step reduces outputs to inputs by construction: the coordinate choice is presented as enabling the procedure, counterterms are fixed by finiteness requirements in the usual way, and results are computed directly rather than fitted or renamed from prior self-citations. The derivation chain is self-contained against the input geometry and action with no evidence of self-definitional, fitted-prediction, or uniqueness-imported patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract: the central claim rests on the standard equations of Romans supergravity, the validity of the AdS/CFT dictionary for defect geometries, and the applicability of holographic renormalization in the chosen coordinates. No free parameters, invented entities, or ad-hoc axioms are mentioned.

axioms (2)
  • domain assumption The equations of motion of Romans supergravity admit the stated warped AdS_p × S^q solutions that preserve four supercharges and are asymptotically AdS5 or AdS6.
    Invoked when the paper states the relevant geometries and their properties.
  • domain assumption Holographic renormalization can be performed in the coordinate system where the defect geometry has an asymptotically flat boundary.
    Central to the systematic application described in the abstract.

pith-pipeline@v0.9.1-grok · 5755 in / 1493 out tokens · 26278 ms · 2026-06-28T09:14:55.152336+00:00 · methodology

discussion (0)

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Reference graph

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