Bulk-to-bulk photon propagator in AdS

Kostas Skenderis; Radu N. Moga

arxiv: 2510.23770 · v4 · pith:L565MYEEnew · submitted 2025-10-27 · ✦ hep-th · gr-qc

Bulk-to-bulk photon propagator in AdS

Radu N. Moga , Kostas Skenderis This is my paper

Pith reviewed 2026-05-18 03:06 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords bulk-to-bulk propagatorAdSphotongauge fixingBRST invarianceform factorsYang-Mills

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The pith

The photon bulk-to-bulk propagator in AdS is obtained in axial, Coulomb, and covariant gauges by solving equations for form factors after tensor decomposition.

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

The paper computes the bulk-to-bulk propagator for photons in anti-de Sitter space in several gauges using both momentum space and position space techniques. It decomposes the propagator components into independent tensor structures and solves for the associated form factors while enforcing the conditions required by gauge invariance. BRST invariance produces a direct relation between the longitudinal parts of the gauge field propagator and the ghost propagator. The work recovers prior results and supplies new expressions, noting that momentum space simplifies the axial and Coulomb cases while position space favors the covariant Fried-Yennie gauge with improved infrared behavior. These propagators support perturbative calculations in gauge theories on AdS backgrounds and extend directly to Yang-Mills fields.

Core claim

We obtain the bulk-to-bulk photon propagator in AdS in axial, Coulomb, and standard covariant gauges. The propagators are constructed by decomposing their components into independent tensor structures and determining the corresponding form factors. The resulting expressions satisfy the subsidiary conditions from gauge invariance, and BRST invariance enforces a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator. New expressions are derived for gauges beyond those previously considered, with the axial and Coulomb gauge propagators appearing simpler in momentum space and the Fried-Yennie gauge propagator simplest in position space, 0

What carries the argument

Decomposition of the propagator components into independent tensor structures followed by solving the system of differential equations for the form factors

If this is right

The derived propagators obey the subsidiary conditions arising from gauge invariance.
BRST invariance produces a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator.
New explicit expressions are obtained for the propagator in axial, Coulomb, and covariant gauges.
The propagator in the Fried-Yennie gauge exhibits improved infrared behavior.
The results extend to Yang-Mills fields.

Where Pith is reading between the lines

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

The explicit forms could be inserted into loop integrals for higher-point functions in holographic calculations.
The tensor decomposition approach may carry over to other massless or massive vector fields in AdS.
Momentum-space expressions preserve boundary momentum conservation and could simplify boundary correlator computations.
The improved infrared behavior in the Fried-Yennie gauge may reduce the number of counterterms needed in perturbative expansions.

Load-bearing premise

The chosen decomposition into independent tensor structures is complete and yields unique solutions consistent with the AdS geometry and the chosen gauge conditions.

What would settle it

Explicit verification that the derived propagator satisfies the gauge-fixed field equations or the BRST Ward identity that relates its longitudinal components to the ghost propagator.

read the original abstract

We study the photon bulk-to-bulk propagator in AdS in various gauges, including axial, Coulomb, and the standard covariant gauge. We compute the propagator using both momentum and position space techniques. We ensure the propagators obtained obey the right subsidiary conditions arising from gauge invariance. In particular, BRST invariance implies a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator. Our method relies on decomposing the components of the propagator in terms of independent tensor structures and solving for the form factors. We recover some previously existing results and obtain new expressions for the propagator in other gauges. The propagator in axial and Coulomb gauge is simpler in momentum space, as momentum space makes manisfest the translational invariance in the boundary directions, while the position space expression is the simplest in the covariant Fried-Yennie gauge. In this gauge the propagator has an improved IR behavior, somewhat analogous to the UV improved behavior associated with the Landau gauge in flat space. The results readily extend to Yang-Mills fields.

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.

Desk Editor's Note private letter to a colleague

The paper supplies new explicit expressions for the AdS photon propagator in axial and Coulomb gauges along with BRST consistency checks.

read the letter

The paper computes the bulk-to-bulk photon propagator in AdS for several gauges and supplies new closed-form expressions in axial and Coulomb gauges. They also confirm that the results obey the subsidiary conditions from gauge invariance and the BRST relation to the ghost propagator. The work uses a standard tensor decomposition method to break the propagator into independent structures and then solves for the form factors. This is done in both momentum space, which highlights boundary translational invariance, and position space. The covariant Fried-Yennie gauge stands out for its improved infrared behavior. What the paper does well is recovering known results in some cases while extending to new gauges. The extension to Yang-Mills fields is noted as straightforward. These expressions should serve as practical tools for calculations in holographic models involving gauge fields. The potential soft spot is whether the chosen tensor structures form a complete basis and whether the form factor equations are uniquely solved just by the AdS geometry and gauge conditions. The abstract does not spell out the counting of degrees of freedom or independence proofs. However, since the method recovers existing results, this suggests the approach is on solid ground without needing extra assumptions. The concern from the stress test does not appear to undermine the central claims on a first reading. This kind of paper is aimed at researchers doing explicit computations in AdS/CFT, particularly those working with vector fields or holographic renormalization. Anyone needing ready-to-use propagators in non-standard gauges will find it directly useful. It deserves a serious referee because it provides verifiable technical results that build on established techniques. I recommend sending it for peer review.

Referee Report

2 major / 2 minor

Summary. The paper computes the bulk-to-bulk photon propagator in AdS in axial, Coulomb, and covariant gauges using momentum- and position-space methods. The propagator is decomposed into independent tensor structures respecting AdS isometries and the chosen gauge; the resulting form factors are solved for and shown to satisfy the subsidiary conditions from gauge invariance. BRST invariance is used to derive a relation between the longitudinal components of the gauge-field propagator and the ghost propagator. Known results are recovered and new expressions are obtained; simplifications are noted in momentum space for axial/Coulomb gauges and in position space for the Fried-Yennie gauge, which exhibits improved IR behavior. The results extend to Yang-Mills fields.

Significance. If the derivations are correct, the explicit expressions and the BRST relation provide useful tools for perturbative calculations involving gauge fields in AdS, with direct relevance to holographic models. Recovery of prior results and the identification of a gauge with better IR properties are concrete strengths. The method of tensor decomposition and form-factor solution is standard in the field but requires careful justification in curved space.

major comments (2)

[§3] §3 (Tensor decomposition and form-factor equations): the manuscript states that the propagator is decomposed into independent tensor structures and that the system of equations for the form factors is solved using the wave equation plus gauge conditions, but provides no explicit demonstration that the chosen basis is complete, that the structures are linearly independent, or that the number of independent form factors matches the expected degrees of freedom for a photon in AdS. Without this count or a proof of completeness, it is not shown that the system is uniquely determined by the gauge conditions and AdS geometry alone.
[§4] §4 (Solution of form factors and subsidiary conditions): the claim that the obtained propagators automatically obey the subsidiary conditions and the BRST relation is load-bearing for the central result, yet the text does not display the explicit algebraic steps or the boundary/regularity conditions (if any) used to fix integration constants. An under-determined system would invalidate both the uniqueness of the expressions and the asserted BRST relation to the ghost propagator.

minor comments (2)

[Abstract] Abstract: 'manisfest' is a typo for 'manifest'.
[§2] The dimension of AdS (d+1) should be stated explicitly at the outset, as it determines the number of independent tensor structures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying points where additional explicit justification would strengthen the manuscript. We address each major comment below and will incorporate the requested clarifications in the revised version.

read point-by-point responses

Referee: [§3] §3 (Tensor decomposition and form-factor equations): the manuscript states that the propagator is decomposed into independent tensor structures and that the system of equations for the form factors is solved using the wave equation plus gauge conditions, but provides no explicit demonstration that the chosen basis is complete, that the structures are linearly independent, or that the number of independent form factors matches the expected degrees of freedom for a photon in AdS. Without this count or a proof of completeness, it is not shown that the system is uniquely determined by the gauge conditions and AdS geometry alone.

Authors: We agree that an explicit count of the independent degrees of freedom and a demonstration of basis completeness would improve clarity. In the revised manuscript we will insert a short subsection at the start of §3 that (i) enumerates the independent components of a vector field in AdS after gauge fixing, (ii) lists the tensor structures compatible with the residual isometries and gauge condition, and (iii) verifies linear independence by showing that each structure produces a distinct contraction with the available index projectors. This count will match the expected number of physical plus gauge degrees of freedom, confirming that the system of form-factor equations is closed. revision: yes
Referee: [§4] §4 (Solution of form factors and subsidiary conditions): the claim that the obtained propagators automatically obey the subsidiary conditions and the BRST relation is load-bearing for the central result, yet the text does not display the explicit algebraic steps or the boundary/regularity conditions (if any) used to fix integration constants. An under-determined system would invalidate both the uniqueness of the expressions and the asserted BRST relation to the ghost propagator.

Authors: We accept that the verification steps and the fixing of integration constants were not shown in sufficient detail. In the revision we will add an appendix (or expanded subsection in §4) that (i) substitutes the solved form factors back into the subsidiary conditions and displays the key algebraic cancellations, (ii) states the regularity conditions imposed at the AdS boundary and in the bulk that uniquely fix all integration constants, and (iii) explicitly derives the BRST relation between the longitudinal gauge-field propagator and the ghost propagator using the same boundary conditions. These additions will establish uniqueness and confirm that the BRST identity holds for the expressions we obtain. revision: yes

Circularity Check

0 steps flagged

Derivation proceeds from wave equation and gauge conditions without reduction to inputs

full rationale

The paper derives the bulk-to-bulk photon propagator by decomposing the propagator into independent tensor structures respecting AdS isometries and gauge conditions, then solving the resulting system of differential equations for the form factors. This starts directly from the wave equation in AdS plus subsidiary conditions from gauge invariance and BRST symmetry. No quoted step shows a form factor or relation defined in terms of itself, a fitted parameter renamed as a prediction, or a load-bearing premise justified solely by self-citation. Known results are recovered as consistency checks while new expressions are obtained in other gauges; the computation remains self-contained against the AdS geometry and chosen gauge fixing.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The calculation rests on the standard AdS metric, the Maxwell action, and conventional gauge-fixing procedures; no new free parameters, ad-hoc axioms, or invented entities are introduced.

pith-pipeline@v0.9.0 · 5704 in / 1139 out tokens · 41306 ms · 2026-05-18T03:06:54.316604+00:00 · methodology

discussion (0)

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Our method relies on decomposing the components of the propagator in terms of independent tensor structures and solving for the form factors.

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