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REVIEW 4 major objections 3 minor 47 references

"Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model

T0 review · 4 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that replacing bulk Green functions by their harmonic counterparts turns the old self-energy conformal bootstrap on AdS into algebraic equations that yield explicit O(N) conformal dimensions, starting at 1.134 for N = 1…

desk verdict New harmonic-bubble bootstrap in AdS, but the O(N) numerics are wrong: Eq. (31) has N on the wrong side, so the claimed conformal dimensions do not follow. read the letter →

arxiv 1908.05471 v3 pith:JHZTQ6CI submitted 2019-08-15 hep-th

Boris L. Altshuler This is my paper · ORCID
classification hep-th PACS 11.10.Kk11.25.Hf
keywords conformalbootstrapO(N)modelAdS/CFTcorrespondencedimensionsHubbard-StratonovichfieldSchwinger-KeldyshformalismharmonicGreenfunctionsextremalcorrelators
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a version of the old conformal bootstrap can produce numerical predictions when formulated in AdS/CFT. The idea is to demand that a boundary two-point correlator equal the self-energy bubble built from the same bulk fields, and then to simplify the resulting integral equations by replacing each bulk Green function with its harmonic counterpart, the difference of the IR and UV Green functions. In the $O(N)$ symmetric model with a Hubbard-Stratonovich scalar, this simplification reduces the bootstrap to algebraic equations for the conformal dimension of the $N$ fields. Solving those equations gives explicit roots, for example $\Delta_\psi = 1.134$ for $N=1$ in $d=4$, which the author offers as evidence that the approach can predict conformal dimensions, and hence bulk masses, rather than taking them as input. The more speculative steps, in particular the harmonic replacement and the hypotheses about the Hubbard-Stratonovich dimension, are acknowledged in the paper as assumptions rather than derivations.

What carries the argument

The load-bearing object is the harmonic bubble $\widetilde M^{\mathrm{2pt\,bubble}}_{\Delta_{\phi_1}|\Delta_{\phi_2}\Delta_{\phi_3}}(x_1,x_2)$: the two-point bubble diagram built from two bulk-to-boundary propagators and two bulk-to-bulk propagators in which every internal Green function $G^{BB}_\Delta$ has been replaced by $\widetilde G_\Delta = G^{BB}_\Delta - G^{BB}_{d-\Delta}$, the difference of the infrared and ultraviolet Green functions. Through the split representation (9)–(10), this object evaluates to the closed expression (24), involving the symmetric coefficient $R(\Delta_{\phi_1},\Delta_{\phi_2},\Delta_{\phi_3})$ and the function $F(\Delta)$ from (27). The split representation is what collapses the double spectral integrals over $\nu,\nu'$ in the exact equations (22) to residues, turning the bootstrap into the algebraic equations (28) whose roots are listed in Section 4. The intended physical justification for the replacement is a Schwinger-Keldysh, closed-time-path treatment of the AdS/CFT self-energy, whose Keldysh component is built from homogeneous solutions rather than ordinary propagators.

What would settle it

Compute the exact self-energy bootstrap equation (22) for the $O(N)$ model in $d=4$ using the ordinary bulk Green functions of (8) instead of the harmonic ones, and check whether a solution exists with $\Delta_\psi$ near $1.134$ for $N=1$, and near the corresponding roots for $N=2,3$. If the exact equations give no such solution or give substantially different values, then the harmonic replacement that produces (28) is falsified.

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Extended reading notes

Core claim

The paper's central claim is that the self-consistent bootstrap condition for a boundary two-point function, in which the conformal correlator is equated to the bubble diagram built from the same bulk fields, can be reduced to an algebraic equation once each bulk-to-bulk Green function $G^{BB}_\Delta$ is replaced by its harmonic counterpart $\widetilde G_\Delta = G^{BB}_\Delta - G^{BB}_{d-\Delta}$. With that replacement, the harmonic bubble $\widetilde M^{\mathrm{2pt\,bubble}}_{\Delta_{\phi_1}|\Delta_{\phi_2}\Delta_{\phi_3}}(x_1,x_2)$ can be evaluated in closed form, and the bootstrap condition becomes equation (28), $C_{\Delta_{\phi_1}}/P_{12}^{\Delta_{\phi_1}} = \widetilde M^{\mathrm{2pt\,bubble}}_{\Delta_{\phi_1}|\Delta_{\phi_2}\Delta_{\phi_3}}(x_1,x_2)$. Applied to the $O(N)$ model with interaction $g\,\sigma\sum_k\psi_k^2$, the condition produces the spectral equations $N F(\Delta_\psi)=F(\Delta_\sigma)$ for a conformal Hubbard-Stratonovich field ($\Delta_\sigma = d/2 \pm 1/2$) and $N F(\Delta_\psi)=F(2\Delta_\psi)$ for a composite one, where $F(\Delta)=\Gamma(\Delta)\Gamma(d-\Delta)/[\Gamma(\Delta-d/2)\Gamma(d/2-\Delta)]$. Solving these gives the paper's numbers: for example, $\Delta_\psi=1.134$ for $N=1$ in $d=4$, with further real roots for $N=2,3$, and in the composite case roots such as $\Delta_\psi=4/3$ and $7/5$ for $N=1$, together with complex roots for $N=2,3$. The paper presents these numbers as evidence that this version of the old conformal bootstrap can predict conformal dimensions, while leaving the exact integral equations (22) unsolved.

Load-bearing premise

The predicted numbers stand or fall on replacing the bulk propagators inside the self-energy bubble by their harmonic counterparts, $\widetilde G_\Delta = G^{BB}_\Delta - G^{BB}_{d-\Delta}$; the paper itself says the Schwinger-Keldysh justification for this replacement is only suggestive.

Editorial extensions

If this is right

  • The conformal dimension of the $N$ fields is fixed by the algebraic equation $N F(\Delta_\psi)=F(\Delta_\sigma)$ when the Hubbard-Stratonovich field is conformal, and by $N F(\Delta_\psi)=F(2\Delta_\psi)$ when it is composite.
  • In $d=4$ with a conformal sigma field, the roots include $\Delta_\psi=1.134$ for $N=1$, and real pairs for $N=2$ and $N=3$: $(1.052,1.680)$ and $(1.034,1.741)$ respectively.
  • In the composite case in $d=4$, $N=1$ gives $\Delta_\psi=4/3$ and $7/5$, while $N=2$ and $N=3$ give complex conjugate pairs; in $d=3$ the listed roots are real and satisfy the unitarity bound.
  • The exact bootstrap equations (22) are not solved in the paper; the numerical values (33), (38), (39) follow only after the harmonic replacement that produces the simplified equation (28).
  • If this version of the old conformal bootstrap is valid, it offers a route to conformal dimensions, and hence to bulk masses, without fixing them by hand.

Reading between the lines

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

  • Editorial inference: the harmonic replacement is a general prescription for internal lines, so the same residue-collapsing trick should apply to higher-point and higher-spin bubble diagrams; comparing a one-loop four-point function computed with and without the replacement would test the prescription directly.
  • Editorial inference: the complex roots that appear for $N=2,3$ in the composite case (38) are a warning sign that the simplified equations may be describing a nonunitary or unstable configuration; a large-$N$ calculation with the exact equations (22) would show whether these roots survive.
  • Editorial inference: if bulk fermion propagators admit an analogous harmonic split, the same method would produce fermion conformal dimensions, which the paper points toward as a route to explaining the fermion mass hierarchy through bulk boundary conditions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper proposes a holographic version of the old self-energy conformal bootstrap. Starting from the symbolic bootstrap equations (1) and using the AdS/CFT correspondence, the author writes exact spectral bootstrap equations for scalar three-point bulk interactions, Eq. (22). Since these exact equations are divergent and not solved, the paper introduces a simplified equation, Eq. (28), in which bulk Feynman-Witten Green functions are replaced by their harmonic counterparts. The simplification is admittedly based only on "suggestive considerations" involving the Schwinger-Keldysh formalism. With this simplified equation, the author analyzes an O(N) model of N scalar fields interacting with a Hubbard-Stratonovich field σ. In Sec. 4.1, assuming σ has the conformal dimension d/2 ± 1/2, a spectral equation for Δψ is obtained and solved for N=1,2,3 (Eq. (33)). In Sec. 4.2, imposing the extremal relation Δσ = 2Δψ, another spectral equation is obtained and solved (Eqs. (38), (39)). The paper concludes that this AdS/CFT version of the old conformal bootstrap may predict conformal dimensions.

Significance. If the approach worked, it would be an interesting new route to compute conformal dimensions from self-consistency conditions in AdS/CFT, and it explicitly connects the old 1960s bootstrap program with modern holographic techniques. The paper has genuine strengths: it gives explicit analytic expressions for the relevant integrals and coefficients (Eqs. (24)-(27)), it engages carefully with the earlier literature, and it is unusually transparent about the speculative status of the main assumptions, stating in Sec. 3.2 that the Schwinger-Keldysh justification is "just a suggestive considerations" and in the Conclusion that the results rest on "questionable assumptions." Those strengths are, however, undermined by a concrete algebraic error in Sec. 4.1 and by the fact that the simplified bootstrap equation is an unproved conjecture rather than a controlled limit of the exact equations.

major comments (4)
  1. [Sec. 4.1, Eq. (31)] The O(N) factor is placed on the wrong side of the spectral equation. From Eq. (28) together with Eq. (24), the bootstrap equation for one of the ψ fields reads 1 = g_R^2 F(Δψ) R(Δψ,Δψ,Δσ), while the equation for σ, whose right-hand side is multiplied by N as the text states, reads 1 = N g_R^2 F(Δσ) R(Δσ,Δψ,Δψ). Since R is symmetric in its three arguments, Eq. (26), eliminating g_R^2 gives F(Δψ) = N F(Δσ), not the printed N F(Δψ) = F(Δσ). The roots in Eq. (33) solve the printed equation. For the corrected equation in d=4, F(Δ) = (Δ-1)(Δ-2)^2(Δ-3) takes values only in [-1/4,0] for Δ∈(1,3), while F(Δσ) = -3/16; hence for N≥2 the corrected equation F(Δψ) = -3N/16 has no real solution. Thus the claimed O(N) conformal dimensions in (33) for N=2,3 are not consequences of the simplified bootstrap; only the N=1 values survive, and the advertised N-dependence of the O(N) model is not obtained.
  2. [Sec. 3.2, Eq. (28)] The central simplified bootstrap equation (28) is not derived. It is obtained by replacing the bulk Feynman-Witten Green functions in the bubble diagram by their harmonic counterparts (10), and the author explicitly states that the Schwinger-Keldysh justification is "just a suggestive considerations." The exact equations (22) are divergent in some integration directions and are not solved. Therefore all numerical predictions in Sec. 4 are conditional on an unproved replacement, and the paper should clearly label the calculation as a toy model rather than a consequence of AdS/CFT. If the replacement is invalid, the values in (33), (38), and (39) do not follow. This is a load-bearing issue for the paper's central claim that the proposed bootstrap "may predict values of conformal dimensions."
  3. [Sec. 4.2, Eq. (36)] The extremal relation Δσ = 2Δψ is imposed without independent support. The text argues that since σ(Z) ~ Σ ψ_k^2(Z) it can be considered composite and therefore obey the extremal relation. But in an interacting conformal field theory, composite operators generically acquire anomalous dimensions, so the dimension of σ is not simply twice the dimension of ψ; determining that dimension is precisely what the bootstrap should compute. Imposing (36) is an external ansatz that largely predetermines the outcome, and the resulting roots (38) and (39) should be interpreted as consequences of that ansatz, not as predictions of the model. The Conclusion partially acknowledges this by calling (36) a hypothesis, but the distinction needs to be much more prominent.
  4. [Sec. 3.1 and Sec. 4] The bootstrap system is underdetermined: Eq. (22) and its permutations give three equations for four unknowns (Δ1, Δ2, Δ3, g_R^2). The author acknowledges this and reduces the unknowns by imposing (30) or (36). This is acceptable for an exploratory paper, but it means that the numerical results are a direct consequence of those extra inputs, not of the bootstrap equations alone. The missing fourth equation for the coupling constant, which the paper notes, is a structural gap that should be emphasized in the conclusions if the paper is revised.
minor comments (3)
  1. [Sec. 4.1, below Eq. (33)] The statement that the listed conformal dimensions satisfy the unitarity bound 0 < |Δ - d/2| < 1 is imprecise. The standard scalar unitarity bound in d dimensions is Δ ≥ (d-2)/2, not |Δ - d/2| < 1; the latter is a stronger, nonstandard restriction. The text should either state the correct bound or explain the intended window.
  2. [Eq. (22)] The double-spectral integral in (22) uses the same symbol ν for both integration variables, which makes the formulas harder to read. Renaming one variable to, say, ν' would improve clarity, especially since the convergence discussion refers to the directions ν + ν' and ν - ν'.
  3. [Sec. 4.1, Eq. (32)] The roots in (33) are stated without the shadow dimensions 4 - Δψ, although the text says these also satisfy the equation. For reproducibility, either list the shadow roots explicitly or specify the convention for selecting the displayed roots.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the simplified bootstrap equations are self-consistency conditions with the coupling eliminated, and the Hubbard-Stratonovich dimension inputs are stated hypotheses rather than quantities fitted to the predicted roots.

full rationale

The paper's derivation chain is: exact spectral bootstrap equations (22) are replaced, under an explicitly labelled 'suggestive' Schwinger-Keldysh assumption, by the algebraic harmonic-bubble equations (28); using the computed expression (24) for the harmonic bubble gives equations of the form 1 = g_R^2 F(Delta) R(...). Eliminating g_R^2 leaves a spectral equation for Delta_psi, and the reported roots solve that equation. Nothing in this chain is an input-output identity: the O(N) factor is not a fitted parameter, the coupling constant cancels, and the values of Delta_sigma in (30) or the extremality condition (36) are transparently stated hypotheses, not data-fitting. The paper itself labels the results as obtained 'under questionable assumptions' and as a demonstration that the game is worth the candle (Sec. 5), so there is no hidden reduction of the prediction to a fitted input. The self-citations [26,27] support earlier use of harmonic Green functions in tadpole/one-loop computations, but the present simplified bootstrap does not rest on an unverified uniqueness theorem imported from those papers; the cited computations are external and the NEGF justification is independent and admittedly tentative. One non-circularity caveat: Eq. (31) as printed appears algebraically inconsistent with (28)+(24), which would give F(Delta_psi)=N F(Delta_sigma) rather than N F(Delta_psi)=F(Delta_sigma); this would affect the numerical roots in (33), but it is a derivation/correctness problem, not a circularity, so it does not change the score.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The computation pulls in standard AdS/CFT results, a planar bootstrap ansatz, a new harmonic replacement of propagators, and hypotheses about the Hubbard-Stratonovich dimension. There are no fitted parameters, but the number of input assumptions is large.

assumptions (5)
  • domain assumption Planar bootstrap approximation Σ ~ G^2 (Eq. 2)
    The paper adopts the planar diagram approximation for the self-energy, citing Wilson's Nobel Lecture criticism but proceeding anyway (Sec. 1). This is a standard simplification in the old conformal bootstrap literature.
  • ad hoc to paper Harmonic replacement of bulk Green functions in bubble diagrams (Eq. 28)
    The paper replaces G by ~G in the bubble, justified only by 'suggestive considerations' about Schwinger-Keldysh formalism (Sec. 3.2). This is the pivotal unproven step.
  • ad hoc to paper Conformal dimension of the Hubbard-Stratonovich field is d/2 ± 1/2 (Eq. 30) or Δσ = 2Δψ (Eq. 36)
    In Sec. 4.1 the HS field is assumed conformally invariant with known dimension; in Sec. 4.2 it is assumed composite with extremal relation. Neither is derived in the present paper.
  • standard math Standard AdS/CFT dictionary for bulk-to-boundary propagators and spectral representations of Green functions
    Taken from [20,21,36-39], including the split representation (9), (10). These are accepted results in the AdS/CFT literature.
  • domain assumption Regularization of [21] for extremal Witten diagrams (norm-invariant coupling constant, Eq. 34)
    In the extremal case Γ(0) divergences are handled via the prescription of [21]; the paper relies on this without re-deriving it (Sec. 4.2).

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Cite this review

Pith. "Pith review of "Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model." pith.science (2026). https://pith.science/paper/JHZTQ6CI

@misc{pith2026190805471,
  author       = {Pith},
  title        = {Pith review of: "Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JHZTQ6CI}},
  note         = {Machine review of arXiv:1908.05471}
}
abstract

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh formalism is used in AdS/CFT instead of conventional Feynman-Witten diagrams technique, permits to calculate values of conformal dimensions in the $O(N)$ symmetric model with conformal or composite Hubbard-Stratonovich field.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

47 extracted references · 21 canonical work pages

  1. [1]

    Weinberg, ”Model physicist”, Interview to Matthew Chalmers, CERN Courier, Oct 13, 2017, http://cerncourier.com/cws/article/cer n/70138

    S. Weinberg, ”Model physicist”, Interview to Matthew Chalmers, CERN Courier, Oct 13, 2017, http://cerncourier.com/cws/article/cer n/70138

    work page 2017

  2. [2]

    Klebanov and G

    I.R. Klebanov and G. Tarnopolsky, ”Uncolored Random Tensors, Melon Diagrams, and the SYK Models” , Phys. Rev. D 95 (2017) 046004 [ArXiv:hep-th/1611.08915]

    arXiv 2017

  3. [3]

    Klebanov, A

    I.R. Klebanov, A. Milekhin, F. Popov, and G. Tarnopolsky, ”Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics” , Phys. Rev. D 97 (2018) 106023 [ArXiv;hep-th/1802.10263]

    arXiv 2018

  4. [4]

    Sakharov, ”Vacuum Quantum Fluctuations In Curved Space And The Theory Of Gravitation” , Sov

    A.D. Sakharov, ”Vacuum Quantum Fluctuations In Curved Space And The Theory Of Gravitation” , Sov. Phys. Dokl. 12 (1968) 1040 [Dokl. 17 Akad. Nauk Ser. Fiz. 177 (1968) 70]. Reprinted in Gen. Rel. Grav. 32 (2000) 365-367

    work page 1968

  5. [5]

    Polyakov, Zh

    A.M. Polyakov, Zh. Exp. Theor. Fiz. 55 (1968) 1026 [Sov. Phys. JETP 28 (1969) 533]

    work page 1968

  6. [6]

    Migdal, Zh

    A.A. Migdal, Zh. Exp. Theor. Fiz. 55 (1968) 1964 [Sov. Phys. JETP 28 (1969) 1036]; ”Conformal invariance and bootstrap” , Phys. Lett. 37B (1971) 386-388; ”Ancient History of CFT” , http://migdal100.itp.ac.ru/proceedings-files-MigdalAA-AncientHistoryOfCFT.pdf

    work page 1968

  7. [7]

    Parisi and L

    G. Parisi and L. Peliti, Lett. Nuovo Cim. 2 (1971) 627; M. d’Eramo, G. Parisi, and L. Peliti, Lett. Nuovo Cim. 2 (1971) 878; G. Parisi, ”On self- consistency conditions in conformal covariant field theory ”, Lett. Nuovo Cim. 4S2 (1972) 777-780

    work page 1971

  8. [8]

    Fradkin and M.Ya

    E.S. Fradkin and M.Ya. Palchik, Conformal quantum field theory in D dimensions (Kluwer Academic Publ., Dordrecht, 1996); E.S. Fradkin and M.Ya. Palchik, Phys. Report 44C (1978) 249

    work page 1978

Show all 47 references
  1. [9]

    Mack and K

    G. Mack and K. Symanzik, ”Currents, stress tensor and generalized unitarity in conformal invariant quantum field theory” , Comm. Math. Phys. 27 (1972) 247

    1972

  2. [10]

    Mack and T

    G. Mack and T. Todorov, ”Conformal-invariant Green functions without ultraviolet divergences”, Phys. Rev. D 8 (1973) 1764-1787

    1973

  3. [11]

    Dobrev, V.B

    V.K. Dobrev, V.B. Petkova, S.G. Petrova and I.T. Todorov, ”Dynamical derivation of vacuum operator product expansion in Euclide an conformal quantum field theory” , Phys. Rev. D 13 (1976) 887-912

    1976

  4. [12]

    Dobrev, G

    V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova and I.T. Todo rov, ”Harmonic Analysis on the n-Dimensional Lorenz Group and it s Appli- cations to Conformal Quantum Field Theory” , Lecture Notes in Physics, No 63, 280 pages (Springer Verlag, Berlin-Heidelberg-New York, 19 77)

  5. [13]

    Grensing and G

    D. Grensing and G. Grensing, ”Critical indices and the conformal in- variant bootstrap method” , Phys. Rev. D 18 (1978) 2890-2900

    1978

  6. [14]

    Wilson, ”The Renormalization Group and Crit- ical Phenomena” , Nobel Lecture, 8 December 1982, https://www.nobelprize.org/prizes/physics/1982/wilson/lecture/

    K.G. Wilson, ”The Renormalization Group and Crit- ical Phenomena” , Nobel Lecture, 8 December 1982, https://www.nobelprize.org/prizes/physics/1982/wilson/lecture/. 18

    1982

  7. [15]

    Ferrara, A.F

    S. Ferrara, A.F. Grillo, and R. Gatto, ”Tensor representation of con- formal algebra and conformally covariant operator product expansion”, Annals Phys. 76 (1973) 161-188

    1973

  8. [16]

    Polyakov, ”Nonhamiltonian approach to conformal quantum field theory”, Zh

    A.M. Polyakov, ”Nonhamiltonian approach to conformal quantum field theory”, Zh. Exp. Theor. Fiz. 66 (1974) 23-42 [Sov. Phys. JETP 39 (1974) 9-18]

    1974

  9. [17]

    Mack, ”Convergence of Operator Product Expansion on the Vacuum in Conformal Invariant Quantum Field Theory” , Commun

    G. Mack, ”Convergence of Operator Product Expansion on the Vacuum in Conformal Invariant Quantum Field Theory” , Commun. Math. Phys. 53 (1977) 155

    1977

  10. [18]

    Poland, S

    D. Poland, S. Rychkov, and A. Vichi, ”The Conformal Bootstrap: Theory, Numerical Techniques, and Applications” , [ArXiv: hep- th/1805.04405]

    arXiv

  11. [19]

    Alday and A

    L.F. Alday and A. Zhiboedov, ”Conformal Bootstrap With Slightly Broken Higher Spin Symmetry” , JHEP 1606 (2016) 091 [ArXiv:hep- th/1506.04659]

    2016 arXiv

  12. [20]

    Giombi, C

    S. Giombi, C. Sleight, and M. Taronna, ”Spinning AdS Loop Dia- grams: Two Point Functions” , JHEP, 1806 (2018) 030 [ArXiv: hep- th/1708.08404]

    2018 arXiv

  13. [21]

    Giombi, V

    S. Giombi, V. Kirilin, and E. Perlmutter, ”Double-Trace Deforma- tions of Conformal Correlations” , JHEP 1802 (2018) 175 [ArXiv: hep- th/1801.01477]

    2018 arXiv

  14. [22]

    Gubser and I

    S.S. Gubser and I. Mitra, Double-trace operators and one loop vac- uum energy in AdS/CFT , Phys. Rev. D67 (2003) 064018 [ArXiv: hep-th/0210093]

    2003 arXiv

  15. [23]

    Hartman and L

    T. Hartman and L. Rastelli, ”Double-trace deformations, mixed bound- ary conditions and functional determinants in AdS/CFT” , JHEP 0801 (2008) 019 [ArXiv: hep-th/0602106]

    2008 arXiv

  16. [24]

    Diaz and H

    D.E. Diaz and H. Dorn, ”Partition functions and double-trace deforma- tions in AdS/CFT” , JHEP 0705 (2007) 046 [ArXiv: hep-th/0702163]

    2007 arXiv

  17. [25]

    Saharian, Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld , Nucl

    A.A. Saharian, Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld , Nucl. Phys. B 712 (2005) 196 [ArXiv:hep-th/0312092]. 19

    2005 arXiv

  18. [26]

    Altshuler, ”Sakharov’s induced gravity on the AdS background

    B.L. Altshuler, ”Sakharov’s induced gravity on the AdS background. SM scale as inverse mass parameter of Schwinger-DeWitt expans ion”, Phys. Rev. D 92 (2015) 065007 [ArXiv: hep-th/1505.07421]

    2015 arXiv

  19. [27]

    Altshuler, ”Simple way to calculate UV -finite one-loop quantum energy in Randall-Sundrum model” , Phys

    B.L. Altshuler, ”Simple way to calculate UV -finite one-loop quantum energy in Randall-Sundrum model” , Phys. Rev. D 95 (2017) 086001 [ArXiv:hep-th/1701.01541]; ”Scalar field on AdS: quantum one loop ”in one line” , Report at the Ginzburg Centennial Conference, Lebedev In- stitu...

    2017 arXiv

  20. [28]

    Allais, ”Double-trace deformations, holography and the c-conjecture”, JHEP 11 (2010) 040[ArXiv: hep-th/1007.2047]

    A. Allais, ”Double-trace deformations, holography and the c-conjecture”, JHEP 11 (2010) 040[ArXiv: hep-th/1007.2047]

    2010 arXiv

  21. [29]

    Aros, D.E

    R. Aros, D.E. Diaz, ”Determinant and Weyl anomaly of Dirac operator: a holographic derivation” , [ArXiv:math-ph/1111.1463]

    arXiv

  22. [30]

    Keldysh, JETP, 47 (1964) 1515; Sov

    L.V. Keldysh, JETP, 47 (1964) 1515; Sov. Phys., JETP 20 (1965) 1018

    1964

  23. [31]

    Arseev, ”On the nonequilibrium diagram technique: derivation, some features, and applications” , Physics-Uspekhi, 58 (12) (2015)

    P.I. Arseev, ”On the nonequilibrium diagram technique: derivation, some features, and applications” , Physics-Uspekhi, 58 (12) (2015)

    2015

  24. [32]

    Barvinsky, ”Serendipitous discoveries in nonlocal gravity theory” , Phys

    A.O. Barvinsky, ”Serendipitous discoveries in nonlocal gravity theory” , Phys. Rev. D 85 (2012) 104018 [ArXiv:hep-th/1112.4340]

    2012 arXiv

  25. [33]

    Meulen, J

    M. Meulen, J. Smit, ”Classical approximation to quantum cosmological correlations”, JCAP (2007) 0711:023 [ArXiv:hep-th/0707.0842]

    2007 arXiv

  26. [34]

    Akhmedov, ”IR divergences and kinetic equation in de Sitter space

    E.T. Akhmedov, ”IR divergences and kinetic equation in de Sitter space. Poincare patch: Principal series” , JHEP 1201 (2012) 066 [ArXiv:hep- th/1110.2257]; E.T. Akhmedov, F.K. Popov and V.M. Slepukhin, ”In- frared dynamics of the massive φ4 theory on de Sitter space” , Phys. R...

    2012 arXiv

  27. [35]

    D’Hoker, D.Z

    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis, and L. Ras telli, ”Extremal correlators in the AdS/CFT correspondence” , Published in ”The Many Faces of the Superworld: Yuri Golfand Memorial Vol - ume”, Edited by M.A. Shifman, World Scientific Pub Co Inc. 2000 [ArXiv:hep-th...

    2000 arXiv

  28. [36]

    Penedones, ”Writing CFT correlation functions as AdS scattering amplitudes”, JHEP 1103 (2011) 025 [ArXiv:hep-th/1011.1485]

    J. Penedones, ”Writing CFT correlation functions as AdS scattering amplitudes”, JHEP 1103 (2011) 025 [ArXiv:hep-th/1011.1485]. 20

    2011 arXiv

  29. [37]

    Fitzpatrick, J

    A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, B.C. van Re es, ”A Natural Language for AdS/CFT Correlators” , JHEP (2011) 2011:95 [ArXiv:hep-th/1107.1499]

    2011 arXiv

  30. [38]

    Costa, V

    M.S. Costa, V. Goncalves and J. Penedones, ”Spinning AdS Propaga- tors”, JHEP 1409 (2014) 064 [ArXiv:hep-th/1404.5625]

    2014 arXiv

  31. [39]

    Bekaert, J

    X. Bekaert, J. Erdmenger, D. Ponomarev and S. Sleight, ”Towards holo- graphic higher-spin interactions: Four-point functions a nd higher-spin exchange”, JHEP 03 (2015) 170 [ArXiv:hep-th/1412.0016]

    2015 arXiv

  32. [40]

    Freedman, S.D

    D.Z. Freedman, S.D. Mathur, A. Matusis, and L. Rastelli, ”Correla- tion functions in the CFTd/AdSd+1 correspondence”, Nucl. Phys. B 546 (1999) 96-118 [ArXiv:hep-th/9804058]

    1999 arXiv

  33. [41]

    Paulos, ”Towards Feynman rules for Mellin amplitudes in AdS/CFT”, JHEP (2011) 2011:74 [ArXiv:hep-th/1107.1504]

    M.F. Paulos, ”Towards Feynman rules for Mellin amplitudes in AdS/CFT”, JHEP (2011) 2011:74 [ArXiv:hep-th/1107.1504]

    2011 arXiv

  34. [42]

    Symanzik, On calculations in conformal invariant field theories , Lett

    K. Symanzik, On calculations in conformal invariant field theories , Lett. Nuovo Cim. 3 (1972) 734-738

    1972

  35. [43]

    Hogervorst, S

    M. Hogervorst, S. Rychkov, B.C. van Rees, ”Unitarity violation at the Wilson-Fisher fixed point in 4 −ǫ dimensions”, Phys. Rev. D93 (2015) 125025 [ArXiv:hep-th/1512.00013]

    2015 arXiv

  36. [44]

    Metsaev, ”Light-cone continuous-spin field in AdS space” [ArXiv:hep-th/1903.10495]

    R.R. Metsaev, ”Light-cone continuous-spin field in AdS space” [ArXiv:hep-th/1903.10495]

    1903 arXiv

  37. [45]

    Randall, R

    L. Randall, R. Sundrum, ”A Large Mass Hierarchy from a Small Extra Dimension” , Phys.Rev.Lett. 83:3370-3373 (1999) [ArXiv: hep-ph/9905221]

    1999 arXiv

  38. [46]

    Grossman and M

    Y. Grossman and M. Neubert, ”Neutrino masses and mix- ings in non-factorizable geometry” , Phys. Lett. B474 (2000) 361 [ArXiv:hep-ph/9912408]

    2000 arXiv

  39. [47]

    Gherghetta and A

    T. Gherghetta and A. Pomarol, ”Bulk fields and supersymmetry in a slice of AdS”, Nucl.Phys. B586 (2000) 141162 [ArXiv: hep-ph/0003129]. 21

    2000 arXiv

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