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UV/IR Relations in AdS Dynamics

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ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Amanda W. Peet, Joseph Polchinski

High Energy Physics - Theory · Submitted 3 Sep 1998 · 24 references

Pith's verdict: A clean, honest clarification note that separates the holographic and stretched-string UV/IR maps; the p=6 section is the only place it asserts more than it shows.

T0 · AI review

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arXiv IDhep-th/9809022 (version 2)
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CitationAmanda W. Peet, Joseph Polchinski. "UV/IR Relations in AdS Dynamics." arXiv:hep-th/9809022 (1998). https://pith.science/paper/HJEWAWZG
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The paper

The paper claims

The AdS/CFT correspondence has been used with two different energy–distance relations, and this paper shows they agree only in conformal backgrounds: for nonconformal Dp-brane throats they differ in functional form, which changes which of a

The reading

The paper sets out to separate two distance–energy relations that were being used almost interchangeably in the AdS/CFT correspondence, and to work out what happens when the background is not conformally invariant. One relation comes from the supergravity wave equation and ties the radial position $U$ to an energy $E$; the other comes from the energy of a string stretched out to a brane probe sitting at $U$. In the conformal D3, M5 and M2 cases both are linear in $U$ and differ only by normalization, so nothing turns on the choice. For nonconformal Dp-brane throats the two relations have different functional forms, and the authors follow that difference through the effective-coupling analysis of those backgrounds to see which description is weakly coupled where. The payoff is a re-reading of the known phase diagram: the earlier analysis holds for brane probes, and the supergravity-probe version has to be redone, with new behavior at $p=5$ and $p=6$.

What carries the argument

The load-bearing device is the wave equation for a massless scalar of angular momentum $ell$ minimally coupled to the Einstein-frame Dp metric, Eq. (2.14). Its two competing terms — the angular barrier going as $U^{-2}$ and the momentum term $k^2 g^2_{YM} N U^{7-p}$ — balance at a radius that defines the holographic energy–radius map, and this same 'all metric terms scale together' criterion reproduces the conformal results and the black-hole temperature/radius relation. The competing map is the stretched-string energy: the world-sheet measure cancels the string tension so that the energy equals the coordinate length $U$ for a D3 probe, generalizing to $tau = U^2$ for an M2-brane ending on an M5-brane. Comparing the two maps through the effective coupling is what produces the case analysis by $p$.

Extended reading notes

Core claim

The central claim is that 'the AdS/CFT distance–energy relation' is not one thing. The holographic relation, read off from the scaling of the minimally coupled scalar wave equation (equivalently, from requiring that the two terms of the metric share a common scaling), gives $E = U^{(5-p)/2}/(g_{YM}N^{1/2})$ for a Dp-brane throat, while a stretched string ending on a probe brane gives $E = U$. For $p=3$ these coincide up to normalization; for other $p$ they do not, and the effective gauge coupling $g^2_{eff} = g^2_{YM} N E^{p-3}$ therefore runs differently depending on which probe is doing the measuring. The authors show that for $p le 4$ the weak-coupling conditions agree for both probes, so the existing catalogue of effective descriptions survives; at $p=5$ the holographic relation degenerates and the boundary theory loses renormalized local operators, the field spread growing as $g_{YM}N^{1/2}ln(U_0/U)$; at $p=6$ the supergravity probe's radius decreases with energy, giving a gauge theory near the origin and a supergravity theory far away that are isolated from one another. They also check that the holographic entropy formula reproduces the nonextremal Dp-brane entropy at temperature $T=E$.

Load-bearing premise

The whole case analysis rests on taking the radius at which the two terms of the scalar wave equation balance — equivalently, where all terms in the metric scale alike — as the definition of the holographic energy–radius map; if the relevant localization scale were set by something else, such as the full Green's function rather than the scaling of the wave operator, the functional forms in Eq. (2.15) and the weak-coupling comparisons built on them would change.

Editorial extensions

If this is right

  • For $p le 4$ the earlier effective-description catalogue stands for both kinds of probe, because $g^2_{eff} ll 1$ holds for both at the same radii.
  • For $p=5$ holography fails sharply: boundary data must scale as $U^{(g^2_{YM}Nk^2)^{1/2}}$ to give a finite result, which has no Fourier transform, so renormalized local operators do not exist.
  • For $p=6$ the apparent paradox of two weakly coupled descriptions at once is resolved by isolation: the gauge theory sits at $U^3 < g_{YM}^{-2}N^{-1}$ and the supergravity at $U^3 > g_{YM}^{-2}N^{-1}$, with no overlap.
  • The holographic entropy $S = L^p E^{(9-p)/(5-p)} N^2 [g^2_{YM}N]^{(p-3)/(5-p)}$ matches the nonextremal Dp-brane entropy at $T=E$, extending the D3 result to all $p$.
  • For $p=1$ the apparent gap left by the brane-probe relation is not a real gap, because at those scales the D-string probe is replaced by an $ilde F$-string description and the scale $E=U$ loses its meaning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The distinction suggests a general diagnostic: whenever a duality map is used to compare weak-coupling regimes, one should check whether both sides are using the same probe type, since the two maps agree only when the background is conformal.
  • The $p=5$ loss of local operators looks like a clean example of a holographic dual that exists in momentum space but not in position space; it would be worth asking whether that momentum-space theory is still local in any weaker sense.
  • The $p=6$ isolation argument implies that 'two weakly coupled descriptions of one system' is not by itself a contradiction provided the sectors decouple, a criterion that could be applied to other suspected duality paradoxes.
  • If the holographic map is the one governing thermodynamics, then the brane-probe energy $E=U$ is best read as a self-energy scale rather than a cutoff, matching the interpretation of the stretched string as a heavy external charge.
Original abstract

We point out that two distinct distance--energy relations have been discussed in the AdS/CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,852 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.56 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We point out that two distinct distance--energy relations have been discussed in the AdS/CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We point out that two distinct distance--energy relations have been discussed in the AdS/CFT correspondence. background 0.54 0.45 0.13 asserted 1.00
s1 In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. result 0.73 0.17 0.30 asserted 1.00
s2 We discuss the relation to probe processes, the holographic principle, and black hole entropies. contribution 0.98 0.77 0.12 asserted 0.56

What kind of paper the classifier reports this is: position or commentary 0.78 · evidence from argument 0.78.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References
How later papers used it

90 later papers cite it

Evidence: substantial. 90 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 113 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 2 papers with this label
Cites it as support 1 of 3 papers with this label

  • Said its result is consistent with this paper's expectation that particle wave-functions are localized in the supergravity regime around the radial position corresponding to their compositeness scale.

    Metastable Vacua in Warped Throats at Non-Isolated Singularities (2010) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

86 arXiv papers cite this in 109 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 80 sentences without a confident label

Uses its method or tool 2 papers
  • Nevertheless it is possible to use the results in [ref] to evaluate the on-shell action of the spherical brane solutions and reproduce the scaling of the free energy with $N$ and $λ_eff$ in [ref].

    Spherical Branes · Introduction · 0.95

  • Indeed, following [ref] one considers the s-wave mode of a massless scalar field on the background [ref].

    Gravitational solitons and non-relativistic string theory · Regime of validity of the near-horizon fundamental string soliton · 0.85

Cites it as support 3 papers
  • This is in line with the prediction by Peet and Polchinski that there are two distinct phases for SYM in seven dimensions, one of them being gravitational [ref] .

    Seven-dimensional super Yang-Mills at negative coupling · Introduction and summary · 0.97

  • The salient feature which establishes this interpretation is that the Wightman functions of LSTs can be shown to have the exponential growth characterstic of the Hagedorn density of states [ref] .

    UV properties of Galileons: Spectral Densities · The case of Little String Theory · 0.98

  • Happily, this is consistent with the expectation that particle wave-functions are localized in the supergravity regime around the radial position corresponding to their compositeness scale [ref] .

    Metastable Vacua in Warped Throats at Non-Isolated Singularities · Cascade · 0.97

Cites it as background 24 papers
  • This goes by the name “Domain Wall/QFT correspondence" [ref] .[Henceforth labeled “DW/QFT" for short.] The fact that the metric ([ref]) is conformal to AdS can be phrased as crucial to the duality, which was established by decoupling the near-horizon dynamics of non-conformal D-branes: passage to a conformal, so-called “dual" frame in which the D-brane near-horizon metric becomes AdS$_p+2×S^8-p$ reveals a manifest $(p+2)$-dimensional gravitational description, in which we identify the radial direction with the energy scale of the dual field theory [ref] .

    Domain Wall Holography for Finite Temperature Scaling Solutions · Introduction and summary · 0.90

  • For systems with a gravity dual, the AdS/CFT correspondence [ref] provides a striking geometric picture for the renormalization group flow and the resulting low energy behavior; the radial direction in the bulk can be associated with the energy scale of the boundary theory [ref] , and the radial flow in the bulk geometry can be interpreted as the renormalization group flow of the boundary theory [ref] .

    Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm · Introduction · 0.97

  • In the context of AdS/CFT, there are two existing approaches: Wilson-like holographic RG [ref] and the Jaynes maximization of entropy subject to contraints [ref] .

    Losing the IR: a Holographic Framework for Area Theorems · Introduction · 0.95

Discussion

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