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Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics

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L. Girardello, M. Petrini, M. Porrati, A. Zaffaroni

High Energy Physics - Theory · Submitted 16 Oct 1998 · 29 references

Pith's verdict: The interpolating-flow construction and the monotonic c(x) are the durable contributions; the 'new CFTs' claim leans on a 10d lift the paper only calls 'most probably' true, and the Addendum quietly halves it.

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arXiv IDhep-th/9810126 (version 5)
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CitationA. Zaffaroni, L. Girardello, M. Petrini, M. Porrati. "Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics." arXiv:hep-th/9810126 (1998). https://pith.science/paper/QAD4SN26
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The paper

The paper claims

Two non-supersymmetric AdS5 stationary points of five-dimensional gauged supergravity are argued to be new local conformal field theories, connected to N=4 super Yang-Mills by interpolating holographic renormalization-group flows.

The reading

The paper works inside the Maldacena correspondence, which maps a four-dimensional conformal field theory to a higher-dimensional gravity theory living on anti-de Sitter space. The maximally symmetric case is N=4 super Yang-Mills dual to Type IIB string theory on AdS5 times a five-sphere. The authors ask whether one can deform that theory and land on a different conformal fixed point in the infrared. They look at the five-dimensional N=8 gauged supergravity that comes from reducing Type IIB on the sphere. Its scalar potential has, besides the fully symmetric minimum, two other stationary points where a single scalar gets a vacuum expectation value: one preserves an SO(5) symmetry, the other an SU(3) times U(1). Because both are still anti-de Sitter, the boundary theory is automatically conformally invariant. The authors then write down a radial ansatz with one scalar rolling between the new minimum and the old one, and argue that such interpolating solutions exist because the scalar behaves like a damped particle rolling off a maximum of the inverted potential. Reading the radial coordinate as an energy scale turns this into a renormalization-group flow from the new infrared theory up to N=4 in the ultraviolet, and gives a monotonic central-charge function. Finally, they linearize around the N=4 point for the marginal deformation in the 45 of SU(4) and show, via the Killing spinor equations, that it preserves N=1 superconformal invariance to first order.
Extended reading notes

Core claim

The abstract states: 'We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large N limit,' backed by 'interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points.' If correct, two new conformal fixed points exist and are connected to N=4 by genuine renormalization-group trajectories realized as classical supergravity solutions.

Load-bearing premise

The interpretation of the five-dimensional stationary points as four-dimensional conformal field theories rests on the claim that they lift to full ten-dimensional Type IIB compactifications. Section 4 says of the stationary points that 'they are most probably true compactifications of Type IIB supergravity [16, 17].' The word 'probably' is doing load-bearing work: locality and the CFT interpretation are argued from these lifts, and the paper does not construct the ten-dimensional solution itself.

Original abstract

We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large $N$ limit. We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments.

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, 3,662 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large $N$ limit. We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments.

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 find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large $N$ limit. result 0.93 0.96 0.72 asserted 1.00
s1 We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. contribution 0.73 0.95 0.18 asserted 1.00
s2 We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. contribution 0.96 0.92 0.07 asserted 0.84
s3 We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments. result 0.87 0.89 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v5
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

Figures
Figure 1. KK scalar states with zero or negative mass square.
Figure 2. Shape of the SO(5)-symmetric upside-down potential −V (λ); units on the coordinate axis are conventional small perturbation such that cosh(4λ) < 2 at x = −∞ gives rise to a λ(x) that rolls towards λ = 0, and stops there at x = +∞. The shape of the potential −V (λ) is shown in
Figure 3. Shape of the SU(3) × U(1)-symmetric upside-down potential −V (λ) the series. In the first example we examined, we gave a nonzero expectation value to a supergravity scalar in the 20 of SU(4). This scalar has AdS mass square equal to −4. Using the correspon￾dence between supergravity fields and composite operators in N=4 established in the previous Sections, we identify this perturbation with a composite operator of N=4 super Yang Mills of dimension 2: a mass term for the scalars φi , symmetric and traceless in the index i. Thus the perturbation breaking SO(6) to SO(5) is: O = ǫ X 5
Figure 4. Products of harmonics in the fermion variations ar

Figures reproduced from arXiv:hep-th/9810126 by the authors.

References
How later papers used it

129 later papers cite it

Evidence: substantial. 126 of the citing papers share no author with it, and 8 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 171 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 4 papers with this label
Compares with it 1 of 3 papers with this label

  • Said that its analysis is equivalent to this paper's, provided the central charge function is identified as c(z) ∼ (T_zz)^-5/2.

    A new 6d fixed point from holography (2016) · 0.85 · paraphrased: the licence does not allow quoting

How the literature uses it

124 arXiv papers cite this in 164 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 · 103 sentences without a confident label

Uses its method or tool 4 papers
Compares with it 3 papers
  • Furthermore, we will find that the beta function associated to the dimensionless coupling, $g_L = L^d-Δ$, is proportional to the derivative of the prepotential, $W'$, as opposed to the usual holographic beta function $W'/W$ [ref] .

    Dimensional regularization for holographic RG flows · Introduction · 0.97

  • Notice that this analysis is equivalent to that of [ref] , provided that we identify the central charge function as $c(z) ∼ (T_zz)^-5/2$.

    A new 6d fixed point from holography · Introduction · 0.85

  • Thus there is less sensitivity to the bulk geometry is the present construction of a holographic c-theorem using the entanglement entropy than in the original discussions [ref] .

    Comments on Holographic Entanglement Entropy and RG Flows · Discussion · 0.87

Cites it as support 1 paper
  • Indeed, the $κ_hol$ in the holographic model decreases under any RG flow thanks to the holographic $c$-theorem [ref] that provides the constraint $L_UV ≥L_IR$ for the AdS radii in the UV and IR fixed points.

    Entanglement Entropy of Annulus in Three Dimensions · Universal behaviors · 0.98

Cites it as background 49 papers
  • Considerable progress on constructing $c$-functions has been made from the holographic perspective: Various holographic $c$-theorems have been established in this context by making use of the Null Energy Condition (NEC) [ref] , as well as using the entanglement entropy perspective to analyze holographic RG flows [ref] .

    $c$-functions in Higher-derivative Flows Across Dimensions · Introduction and summary · 0.93

  • For the classical renormalization group flows, [ref] established a c-theorem, demonstrating that so long as the bulk geometry satisfied a suitable energy condition, the c-function of [ref] would be monotonically decreasing along the flow from the UV to the IR (see also [ref] ).

    Reversing Renormalization-Group Flows with AdS/CFT · Introduction · 0.90

  • Here we begin with a review of the holographic c-theorem as originally studied by [ref] for Einstein gravity.

    Comments on Holographic Entanglement Entropy and RG Flows · Review of holographic c-theorems · 0.99

Discussion

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