Pith. sign in

REVIEW 4 major objections 5 minor 35 references

Holographic cosmology predicts vanishing scalar-monopole non-Gaussianity at one loop, but a nonzero tensor-monopole signal.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-31 04:11 UTC pith:IBE5MNTG

load-bearing objection Solid 1-loop ⟨TJJ⟩ with clean soft-limit factorization; the headline f_NL numbers rest on an unproven extension of Sl(2,Z) through contact terms. the 4 major comments →

arxiv 2607.24989 v1 pith:IBE5MNTG submitted 2026-07-27 hep-th gr-qc

Cross-Correlations of Metric and Monopole Perturbations from Holographic Cosmology

Matheus Cravo , Juliana Z. Finotti , Horatiu Nastase This is my paper
classification hep-th gr-qc
keywords holographic cosmologynon-Gaussianitymagnetic monopolesthree-point functionssqueezed limitstress-energy tensorglobal currentsSl(2,Z) duality
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper computes the one-loop three-point function of the stress-energy tensor with two SO(3) global currents in a three-dimensional toy model used for holographic cosmology. Through the holographic dictionary and an Sl(2,Z) duality that maps electric currents to magnetic vortex currents dual to bulk monopoles, the correlator becomes the cross-bispectra of metric perturbations with the monopole field. Semi-local contact terms are required so that the cosmological correlators factorize exactly in the squeezed limit. The resulting effective nonlinearity for scalar-monopole correlations vanishes at this order, while the angle-averaged tensor-monopole parameter is nonzero. The hierarchy of amplitudes matches expectations and supplies a concrete, if distant, observational target for the framework.

Core claim

After including the semi-local contact terms needed for consistent factorization, the squeezed-limit effective parameters extracted from the dual ⟨TJJ⟩ correlator are f_NL^{ξ Ã Ã}=0 at one loop and angle-averaged f_NL^{γ Ã Ã}=6. The scalar channel cancels because the monopole power spectrum scales as 1/p, so its logarithmic derivative exactly offsets the leading factor; the tensor channel survives after angular averaging of the projector contractions.

What carries the argument

The full one-loop ⟨TJJ⟩ (triangle diagram plus contact terms generated by functional differentiation with respect to metric and current sources), converted by the holographic dictionary and Sl(2,Z) electric-to-vortex duality into the cosmological bispectra ⟨ξ Ã Ã⟩ and ⟨γ Ã Ã⟩ in the soft limit.

Load-bearing premise

The claim holds only if the phenomenological holographic dictionary that equates three-dimensional QFT correlators to bulk cosmological correlators remains valid for monopole fields even in the early non-geometric phase.

What would settle it

A two-loop evaluation of the current two-point function that preserves the soft-limit factorization but produces a nonzero f_NL^{ξ Ã Ã} of order the effective coupling, or a future observational constraint on metric-monopole cross-bispectra that contradicts the predicted values 0 and 6 and their amplitude hierarchy.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Scalar-monopole cross-correlations remain unobservable at leading order, so any search should focus on the tensor-monopole channel.
  • The amplitude hierarchy ⟨ξ Ã Ã⟩ ≫ ⟨γ Ã Ã⟩ is preserved because the observed tensor power spectrum is much smaller than the scalar one.
  • Higher-loop corrections can generate a nonzero scalar-monopole f_NL proportional to the effective dimensionless coupling.
  • Contact terms are mandatory for the dual QFT to reproduce the expected cosmological factorization in the squeezed limit.
  • The same setup can be extended to a U(1) current to estimate mixed scalar-scalar-monopole non-Gaussianity.

Where Pith is reading between the lines

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

  • If the soft factorization structure survives at higher loops, the vanishing of f_NL^{ξ Ã Ã} is only a one-loop accident and becomes a clean diagnostic of the running of the monopole spectrum.
  • The angle-averaged value 6 is a sharp, essentially parameter-free number once the projectors are contracted, giving a distinctive target if primordial tensors and monopole relics could ever be cross-correlated.
  • Switching from SO(3) to a U(1) current, as the paper itself flags, would open a larger mixed correlator closer to conventional bispectrum searches.
  • The necessity of contact terms shows that holographic cosmology is sensitive to the precise operator definition of boundary correlators, not merely to connected Feynman diagrams.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript computes the one-loop three-point function \(\langle TJJ\rangle\) in the bosonic three-dimensional \(SO(3)\) toy model previously used in phenomenological holographic cosmology. It gives the complete tensor decomposition and Feynman-parameter integrals, derives the semi-local contact terms required by the source definition of \(T_{\mu\nu}\), and checks the transverse Ward identity. In the soft \(T\)-momentum limit the result reduces to a differential operator acting on \(\langle JJ\rangle\). The authors then apply \(SL(2,\mathbb Z)\) current duality and the holographic dictionary to obtain squeezed-limit \(\langle\xi\tilde A\tilde A\rangle\) and \(\langle\gamma\tilde A\tilde A\rangle\), reporting \(f_{NL}^{\xi\tilde A\tilde A}=0\) at leading order and \(f_{NL}^{\gamma\tilde A\tilde A}=6\).

Significance. If the holographic and duality steps are justified, this is the first mixed metric–monopole non-Gaussianity calculation in this toy framework and gives sharp, falsifiable squeezed-limit outputs. The explicit QFT calculation is a substantial strength: the one-loop integrals are finite and worked out in detail, complete form factors are supplied, contact terms are derived rather than inserted ad hoc, and the result passes a nontrivial transverse Ward-identity and soft-consistency check. The cosmological interpretation, however, remains conditional on the phenomenological dictionary, the Moore–Penrose prescription, and an extension of current duality beyond the two-point-function setting in which it is cited.

major comments (4)
  1. [§3.2, Eqs. (3.18)–(3.19)] The passage from Eq. (3.18) to Eq. (3.19) is asserted by applying S-duality “on both sides.” Refs. [32–34] establish the quoted transformation for current two-point functions, whereas here there is a stress-tensor insertion and the semi-local contact terms of Eq. (3.3), derived from the electric generating functional. Their dual images are not computed, and no Ward-identity check is given for \(\langle T\tilde J\tilde J\rangle\). This is quantitative: the constants “1” and “7” in the headline \(f_{NL}\) values originate from these contact structures. Please derive the dual contact/soft identity, including its extension to the \(SO(3)\) current, or isolate it as an additional assumption and demonstrate robustness.
  2. [Eqs. (3.41), (4.3)–(4.4)] The identification of \(f_{NL}^{\gamma\tilde A\tilde A}\) does not follow unambiguously from the displayed result. Eq. (3.41) gives \(-(\delta^{ab}/15)P_\gamma P_{\tilde A}(7+pP'_{\tilde A}/P_{\tilde A})\). Using Eq. (4.3) literally therefore gives \(-(7+pP'/P)/15=-2/5\), not \(6\). The draft drops \(-1/15\) without specifying a normalization or kinematic convention; Eq. (2.36) explicitly leaves such factors open. Please define the polarization contractions, angle average, and normalization of this mixed \(f_{NL}\), and correct the quoted sign and magnitude accordingly.
  3. [§2.3, Eqs. (2.43)–(2.51)] Eq. (2.45) gives \(P_{\tilde A}(p)=-\pi^2N^2/(2p)\), and Eq. (2.51) consequently gives a negative dimensionless power spectrum. For a Hermitian bulk field, the Wightman two-point function is positive semidefinite; the suggestion that this measures monopole size does not resolve the issue. The sign also affects the interpretation of factorization, the extracted \(f_{NL}\), and the amplitude hierarchy. Please identify whether a sign, operator normalization, analytic continuation, or missing inverse in the holographic formula is responsible before calling this object a power spectrum.
  4. [§4, Eq. (4.5)] The conclusion states \(\langle\xi\tilde A\tilde A\rangle\gg\langle\gamma\tilde A\tilde A\rangle\) because \(P_\gamma\ll P_\xi\). At the order actually computed, however, \(f_{NL}^{\xi\tilde A\tilde A}=0\), while the tensor-monopole correlator is nonzero. Thus the displayed hierarchy is not respected by the paper’s leading-order results; it cannot be inferred from the power spectra after setting the scalar coefficient to zero. The abstract and §4 should either correct the hierarchy statement or provide a quantitative estimate of the subleading scalar contribution.
minor comments (5)
  1. [Eq. (2.43)] The first equality appears to omit the inverse of the QFT two-point function required by Eq. (2.28), although the surrounding text says that the resulting operator is inverted. Please make the reciprocal and its pseudo-inverse prescription explicit.
  2. [After Eq. (3.13)] The text says that the transverse Ward identity is derived in Appendix C, but the derivation is in Appendix A.2.
  3. [§§1–2.3] The introduction uses \(\zeta\) for the scalar metric perturbation, while the calculations use \(\xi\). If these denote the same quantity, please state the convention at first use.
  4. [§3.2, Eqs. (3.16) and (3.34)–(3.41)] The extension from the collinear parametrization (3.16) to the angle-averaged result is plausible because the soft QFT expression is finite and \(p_1\)-independent, but the manuscript should state explicitly that this is why varying only the limiting direction of \(p_1\) in Eq. (3.34) is legitimate.
  5. [General] There are several typographical or index issues: “higly,” “magnitudde,” “aultralocal,” “Figure Figure 1,” “Feynmann,” “then” for “than,” and \(J^d\) in Eq. (3.25) where the external index appears to be \(b\).

Circularity Check

1 steps flagged

No significant circularity: f_NL values are genuine outputs of an explicit 1-loop integral plus soft-limit algebra, not tautologies of a fit or self-definition.

specific steps
  1. self citation load bearing [Sec. 2.2–2.3, eqs. (2.44)–(2.45), (2.49); Sec. 3.2 eqs. (3.19)–(3.22)]
    "the amplitude of the vortex power spectrum was calculated holographically using the electric Noether current J^a_μ within our toy model in [24]... P_Ã(p)=−π²N²/(2p)... Replacing the explicit holographic results at 1-loop, we find ... =0."

    P_Ã and the toy-model 2-pt data are imported from the authors' prior monopole paper and used unchanged to evaluate D(p)=1+pP'/P. This is ordinary reuse of a fixed input, not a fit to the new cross-correlators and not a uniqueness claim that forbids alternatives; the new content is the ⟨TJJ⟩ integral and soft-limit extraction. Flagged only as minor background self-citation load (score contribution 1), not as a reduction of the f_NL claim to a tautology.

full rationale

The central claims f_NL^{ξÃÃ}=0 and angle-averaged f_NL^{γÃÃ}=6 follow from (i) an explicit 1-loop triangle evaluation of ⟨TJJ⟩_flat, (ii) addition of semi-local contact terms derived from the generating-functional definition, (iii) the soft-limit identity (3.17) obtained by expanding the form factors, and (iv) projector algebra on the holographic map. At 1-loop P_Ã∝1/p forces D(p)=1+d log P_Ã/d log p=0 for the scalar channel and, after θ-averaging of the tensor contractions, the number 6 for the tensor channel. These are not fitted to the target observables, nor defined in terms of themselves. Prior self-citations supply the holographic dictionary, the toy model, the electric 2-pt function, and P_à as fixed inputs; they do not re-enter as a uniqueness theorem that forces the new f_NL numbers. The open question whether Sl(2,Z) legitimately maps the contact-term-completed mixed 3-pt function (raised by the skeptic) is a correctness/validity concern about an unproven extension of a 2-pt duality, not a circular reduction of the derivation to its inputs. N≃3000 from CMB is used only for optional amplitude scale-setting and does not enter the f_NL coefficients. Score 1 only for ordinary background self-citation load that is not load-bearing for the claimed prediction.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 1 invented entities

The central f_NL claims rest on the holographic cosmology dictionary, Sl(2,Z) current duality, a specific bosonic SO(3) toy model, a choice of analytic continuation (Ψ=Z), and the inclusion of semi-local contact terms in the definition of ⟨TJJ⟩. No new free parameters are fitted in this paper; N and g_eff enter only through prior matching. Invented bulk entities (monopole field dual to vortex current) are inherited from the authors’ earlier monopole-problem paper.

free parameters (2)
  • N (rank of dual gauge group) = ~3000 (from prior CMB matching)
    Fixed in prior holographic-cosmology CMB fits to N≈3000; used here only to quote dimensionless power spectra, not refit.
  • g_YM / g_eff
    Effective coupling of the 3d toy model; 1-loop results are leading order in g_eff, with 2-loop schematic dependence shown but not computed.
axioms (6)
  • domain assumption Holographic dictionary equating cosmological n-point functions of metric and monopole fields to (analytically continued) QFT correlators of T and J/tilde J, including pseudo-inverses of transverse projectors.
    Assumed throughout §2.3 and eqs. 2.28–2.59; justified by citation to McFadden–Skenderis and wavefunction approaches, not re-derived.
  • domain assumption Sl(2,Z) duality maps the electric Noether current two-point function to the magnetic vortex current dual to bulk monopoles (t o 1/t when ω=0).
    Used to convert ⟨JJ⟩ into ⟨tilde J tilde J⟩ and hence P_Ã; taken from Witten/Herzog et al. and prior Nastase monopole paper.
  • ad hoc to paper The bosonic SO(3) adjoint scalar+gauge toy model (eq. 2.20) is representative enough that its ⟨TJJ⟩ controls cosmological monopole–metric cross-correlations.
    Chosen as simplest vortex-admitting model preferred by CMB fits; fermions set to zero; potential independence claimed only for anomalous dimension, not fully for ⟨TJJ⟩.
  • domain assumption Analytic continuation bar N = i N, bar p = i p corresponds to Ψ=Z (not Ψ*=Z) and is the correct map for real cosmological correlators.
    Stated in §2.3 citing Bzowski–McFadden–Skenderis; alternative continuation is said to agree but is not re-checked here for ⟨TJJ⟩.
  • domain assumption Full ⟨TJJ⟩ must include semi-local contact terms from metric/current sources (eq. 3.3); ultralocal triple-coincidence terms may be dropped as scheme-dependent.
    Derived in App. A from generating-functional definitions; necessary for squeezed factorization and Ward identity.
  • standard math Standard dimensional regularization and Feynman parametrization of 3d one-loop tensor integrals are valid and finite for this model.
    Used throughout Apps. B–C; UV/IR finiteness claimed and used to drop regulator dependence.
invented entities (1)
  • Bulk magnetic monopole field à dual to boundary vortex current tilde J no independent evidence
    purpose: Provides the cosmological operator whose cross-correlations with ξ and γ are the paper's observables.
    Inherited from the holographic monopole-problem setup; not independently detected. Falsifiable only if monopole non-Gaussianities or dilution signatures were observed.

pith-pipeline@v1.2.0-grok45-kimik3 · 43985 in / 4463 out tokens · 63645 ms · 2026-07-31T04:11:32.352640+00:00 · methodology

0 comments
read the original abstract

In this paper, we present the 1-loop calculation of the three-point function $\langle TJJ \rangle$ of the stress-energy tensor and two insertions of $SO(3)$ global currents, using a 3d toy model for holographic cosmology. By applying the holographic dictionary that relates these QFT $n$-point functions to cosmological correlators, together with the $Sl(2,\mathbb{Z})$ duality that maps the electric Noether current to a magnetic vortex current dual to cosmological magnetic monopoles, we relate the $\langle TJJ \rangle$ correlator to the cross-correlations between metric perturbations and the bulk magnetic monopole field, specifically mapping to the non-Gaussianities $\langle \xi \tilde{A} \tilde{A} \rangle$ and $\langle \gamma \tilde{A} \tilde{A} \rangle$. We calculate the semi-local contact terms necessary to achieve the exact factorization of the cosmological correlators in the squeezed limit, $p_1 \to 0$. Finally, we evaluate the effective non-linear parameters, showing that the scalar-monopole cross-correlation vanishes at leading order, $f_{NL}^{\xi \tilde{A} \tilde{A}} = 0$, while the tensor-monopole cross-correlation yields a non-zero $f_{NL}^{\gamma\tilde A\tilde A}$. These results respect the expected amplitude hierarchy of the non-Gaussian correlators, while pointing at new directions in which holographic cosmology can be tested experimentally.

Figures

Figures reproduced from arXiv: 2607.24989 by Horatiu Nastase, Juliana Z. Finotti, Matheus Cravo.

Figure 1
Figure 1. Figure 1: Schematic figure illustrating the route taken by the framework [5] to map an accelerating universe to a quantum field theory description. The first step starts from a cosmological spacetime and ends on a domain wall spacetime by a correspondence be￾tween the two. The second step is the holographic description of the domain wall, leading to a 3-dimensional QFT. The last step is to apply the inverse analytic… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

35 extracted references · 34 linked inside Pith

  1. [1]

    The dS / CFT correspondence,

    A. Strominger, “The dS / CFT correspondence,”JHEP10(2001) 034, arXiv:hep-th/0106113

    Pith/arXiv arXiv 2001

  2. [2]

    Non-Gaussian features of primordial fluctuations in single field inflationary models,

    J. M. Maldacena, “Non-Gaussian features of primordial fluctuations in single field inflationary models,”JHEP05(2003) 013,arXiv:astro-ph/0210603

    Pith/arXiv arXiv 2003

  3. [3]

    Quantum gravity in de Sitter space,

    E. Witten, “Quantum gravity in de Sitter space,” inStrings 2001: International Conference. 6, 2001.arXiv:hep-th/0106109

    Pith/arXiv arXiv 2001

  4. [4]

    The World as a hologram,

    L. Susskind, “The World as a hologram,”J. Math. Phys.36(1995) 6377–6396, arXiv:hep-th/9409089

    Pith/arXiv arXiv 1995

  5. [5]

    The Holographic Universe,

    P. McFadden and K. Skenderis, “The Holographic Universe,”J. Phys. Conf. Ser. 222(2010) 012007,arXiv:1001.2007 [hep-th]. [6]DESICollaboration, M. Abdul Karimet al., “DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints,”Phys. Rev. D112 (2025) no. 8, 083515,arXiv:2503.14738 [astro-ph.CO]. [7]DESICollaboration, A. G...

    Pith/arXiv arXiv 2010

  6. [8]

    De Sitter Musings,

    D. Anninos, “De Sitter Musings,”Int. J. Mod. Phys. A27(2012) 1230013, arXiv:1205.3855 [hep-th]

    Pith/arXiv arXiv 2012

  7. [9]

    TASI Lectures on the Cosmological Constant,

    R. Bousso, “TASI Lectures on the Cosmological Constant,”Gen. Rel. Grav.40 (2008) 607–637,arXiv:0708.4231 [hep-th]

    Pith/arXiv arXiv 2008

  8. [10]

    Holography in de Sitter Space via Chern-Simons Gauge Theory,

    Y. Hikida, T. Nishioka, T. Takayanagi, and Y. Taki, “Holography in de Sitter Space via Chern-Simons Gauge Theory,”Phys. Rev. Lett.129(2022) no. 4, 041601, arXiv:2110.03197 [hep-th]

    Pith/arXiv arXiv 2022

  9. [11]

    A microscopic realization of dS 3,

    S. Collier, L. Eberhardt, and B. M¨ uhlmann, “A microscopic realization of dS 3,” SciPost Phys.18(2025) no. 4, 131,arXiv:2501.01486 [hep-th]

    Pith/arXiv arXiv 2025

  10. [12]

    Higher Spin Realization of the dS/CFT Correspondence,

    D. Anninos, T. Hartman, and A. Strominger, “Higher Spin Realization of the dS/CFT Correspondence,”Class. Quant. Grav.34(2017) no. 1, 015009, arXiv:1108.5735 [hep-th]

    Pith/arXiv arXiv 2017

  11. [13]

    Entanglement and Chaos in De Sitter Space Holography: An SYK Example,

    L. Susskind, “Entanglement and Chaos in De Sitter Space Holography: An SYK Example,”JHAP1(2021) no. 1, 1–22,arXiv:2109.14104 [hep-th]

    Pith/arXiv arXiv 2021

  12. [14]

    The Trouble with de Sitter space,

    N. Goheer, M. Kleban, and L. Susskind, “The Trouble with de Sitter space,”JHEP 07(2003) 056,arXiv:hep-th/0212209. 42

    Pith/arXiv arXiv 2003

  13. [15]

    The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization,

    D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, “The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization,” SciPost Phys.11(2021) 071,arXiv:2005.04234 [hep-th]

    Pith/arXiv arXiv 2021

  14. [16]

    Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation,

    N. Kundu, A. Shukla, and S. P. Trivedi, “Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation,”JHEP04(2015) 061, arXiv:1410.2606 [hep-th]

    Pith/arXiv arXiv 2015

  15. [17]

    Holographic Non-Gaussianity,

    P. McFadden and K. Skenderis, “Holographic Non-Gaussianity,”JCAP05(2011) 013,arXiv:1011.0452 [hep-th]

    Pith/arXiv arXiv 2011

  16. [18]

    Holography for Cosmology,

    P. McFadden and K. Skenderis, “Holography for Cosmology,”Phys. Rev. D81 (2010) 021301,arXiv:0907.5542 [hep-th]

    Pith/arXiv arXiv 2010

  17. [19]

    Constraining holographic inflation with WMAP,

    R. Easther, R. Flauger, P. McFadden, and K. Skenderis, “Constraining holographic inflation with WMAP,”JCAP09(2011) 030,arXiv:1104.2040 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  18. [20]

    From Planck data to Planck era: Observational tests of Holographic Cosmology,

    N. Afshordi, C. Coriano, L. Delle Rose, E. Gould, and K. Skenderis, “From Planck data to Planck era: Observational tests of Holographic Cosmology,”Phys. Rev. Lett. 118(2017) no. 4, 041301,arXiv:1607.04878 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  19. [21]

    Renormalisation of IR divergences and holography in de Sitter,

    A. Bzowski, P. McFadden, and K. Skenderis, “Renormalisation of IR divergences and holography in de Sitter,”JHEP05(2024) 053,arXiv:2312.17316 [hep-th]

    Pith/arXiv arXiv 2024

  20. [22]

    Holographic predictions for cosmological 3-point functions,

    A. Bzowski, P. McFadden, and K. Skenderis, “Holographic predictions for cosmological 3-point functions,”JHEP03(2012) 091,arXiv:1112.1967 [hep-th]

    Pith/arXiv arXiv 2012

  21. [23]

    Cosmological 3-point correlators from holography,

    P. McFadden and K. Skenderis, “Cosmological 3-point correlators from holography,” JCAP06(2011) 030,arXiv:1104.3894 [hep-th]

    Pith/arXiv arXiv 2011

  22. [24]

    Holographic cosmology solutions of problems with pre-inflationary cosmology,

    H. Nastase, “Holographic cosmology solutions of problems with pre-inflationary cosmology,”JHEP12(2020) 026,arXiv:2008.05630 [hep-th]

    Pith/arXiv arXiv 2020

  23. [25]

    3-point function of currents for holographic cosmology and monopole non-Gaussianities,

    M. Cravo and H. Nastase, “3-point function of currents for holographic cosmology and monopole non-Gaussianities,”JHEP05(2024) 056,arXiv:2308.13398 [hep-th]

    Pith/arXiv arXiv 2024

  24. [26]

    Naked singularities in dilatonic domain wall space times,

    M. Cvetic and H. H. Soleng, “Naked singularities in dilatonic domain wall space times,”Phys. Rev. D51(1995) 5768–5784,arXiv:hep-th/9411170

    Pith/arXiv arXiv 1995

  25. [27]

    Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence,

    K. Skenderis and P. K. Townsend, “Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence,”J. Phys. A40(2007) 6733–6742, arXiv:hep-th/0610253

    Pith/arXiv arXiv 2007

  26. [28]

    Precision holography for non-conformal branes,

    I. Kanitscheider, K. Skenderis, and M. Taylor, “Precision holography for non-conformal branes,”JHEP09(2008) 094,arXiv:0807.3324 [hep-th]. 43

    Pith/arXiv arXiv 2008

  27. [29]

    Generalized conformal symmetry in D-brane matrix models,

    A. Jevicki, Y. Kazama, and T. Yoneya, “Generalized conformal symmetry in D-brane matrix models,”Phys. Rev. D59(1999) 066001,arXiv:hep-th/9810146

    Pith/arXiv arXiv 1999

  28. [30]

    Two-point function of the energy-momentum tensor and generalised conformal structure,

    C. Corian` o, L. Delle Rose, and K. Skenderis, “Two-point function of the energy-momentum tensor and generalised conformal structure,”Eur. Phys. J. C81 (2021) no. 2, 174,arXiv:2008.05346 [hep-th]

    Pith/arXiv arXiv 2021

  29. [31]

    Magnetic monopoles,

    J. Preskill, “Magnetic monopoles,”Annual Review of Nuclear and Particle Science 34(1984) no. Volume 34,, 461–530.https://www.annualreviews.org/content/ journals/10.1146/annurev.ns.34.120184.002333

    arXiv 1984

  30. [32]

    SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry,

    E. Witten, “SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry,” inFrom Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, pp. 1173–1200. 7, 2003. arXiv:hep-th/0307041

    Pith/arXiv arXiv 2003

  31. [33]

    Particle-vortex and Maxwell duality in theAdS 4×CP 3/ABJM correspondence,

    J. Murugan, H. Nastase, N. Rughoonauth, and J. P. Shock, “Particle-vortex and Maxwell duality in theAdS 4×CP 3/ABJM correspondence,”JHEP10(2014) 051, arXiv:1404.5926 [hep-th]

    Pith/arXiv arXiv 2014

  32. [34]

    Quantum critical transport, duality, and M-theory,

    C. P. Herzog, P. Kovtun, S. Sachdev, and D. T. Son, “Quantum critical transport, duality, and M-theory,”Phys. Rev. D75(2007) 085020,arXiv:hep-th/0701036

    Pith/arXiv arXiv 2007

  33. [35]

    3d QFT IR divergences as UV divergences in 4d Holographic Cosmology,

    M. Cravo and H. Nastase, “3d QFT IR divergences as UV divergences in 4d Holographic Cosmology,”arXiv:2605.16587 [hep-th]

    Pith/arXiv arXiv

  34. [36]

    Soft limits in holographic cosmology,

    P. McFadden, “Soft limits in holographic cosmology,”JHEP02(2015) 053, arXiv:1412.1874 [hep-th]

    Pith/arXiv arXiv 2015

  35. [37]

    Implications of conformal invariance in momentum space,

    A. Bzowski, P. McFadden, and K. Skenderis, “Implications of conformal invariance in momentum space,”JHEP03(2014) 111,arXiv:1304.7760 [hep-th]. 44

    Pith/arXiv arXiv 2014