pith. sign in

arxiv: 2607.00079 · v1 · pith:K6Q3ZR2Dnew · submitted 2026-06-30 · ✦ hep-th · hep-ph

QFT as a set of ODEs: higher dimensions

Fabiana De Cesare , Manuel Loparco This is my paper

Pith reviewed 2026-07-02 18:28 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords AdS/CFT correspondencerelevant deformationsflow equationsboundary operatorsOPE coefficientsmerger-annihilationlevel repulsioncrossing equations
0
0 comments X

The pith

Ordinary differential equations for boundary QFT data under bulk deformations extend from AdS2 to AdS3 and AdS4.

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

The paper generalizes a set of ordinary differential equations that track how scaling dimensions, OPE coefficients, and bulk-boundary coefficients of boundary operators change when a relevant deformation is introduced in the AdS bulk. These equations were first obtained for two-dimensional AdS and are now shown to apply in three and four dimensions after only dimensional adjustments. The same equations automatically reproduce the merging and annihilation of operators once one reaches marginality and the repulsion between nearby scaling dimensions. Practical refinements include swapping the OPE flow equation for the crossing equation and applying Padé approximants to speed up sums over operators. The resulting framework is positioned for later use on strongly coupled theories in higher-dimensional AdS and their flat-space limits.

Core claim

Correlation functions of local operators in AdS are fixed by the boundary QFT data: scaling dimensions Δ_i, OPE coefficients C_ijk, and bulk-boundary coefficients b^Φ̂_i. The ordinary differential equations that govern the variation of this data under a bulk relevant deformation, previously derived only for AdS2, are here generalized to AdS3 and AdS4. These flow equations natively encode merger-annihilation when a boundary operator hits marginality and level repulsion when different Δ_i approach each other. The implementation is improved by replacing the ODE for OPE coefficients with the crossing equation and by using Padé approximants to enhance convergence of sums over boundary operators i

What carries the argument

Ordinary differential equations (ODEs) for the evolution of scaling dimensions Δ_i, OPE coefficients C_ijk, and bulk-boundary coefficients b under a bulk relevant deformation, now extended by dimensional adjustments to AdS3 and AdS4.

If this is right

  • The same ODE structure holds in AdS3 and AdS4 after only dimensional adjustments.
  • Merger-annihilation of boundary operators is reproduced exactly when an operator reaches marginality.
  • Level repulsion between distinct scaling dimensions is reproduced when the dimensions approach each other.
  • Substituting the crossing equation for the ODE governing OPE coefficients increases computational efficiency.
  • Padé approximants improve convergence of sums over boundary operators at least in free theories.

Where Pith is reading between the lines

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

  • The framework could be used to numerically integrate RG flows for boundary theories in higher-dimensional AdS without solving the full bootstrap at each step.
  • The same structural generalization may apply to other bulk geometries beyond AdS or to deformations that include irrelevant operators.
  • In the flat-space limit the flow equations might connect boundary data directly to properties of scattering amplitudes or S-matrices.

Load-bearing premise

The structural form of the flow equations derived for AdS2 carries over to AdS3 and AdS4 with only dimensional adjustments and without new structural terms or obstructions.

What would settle it

An explicit calculation of the exact variation of boundary data under a relevant bulk deformation in a solvable theory such as a free scalar in AdS3, followed by a direct check of whether the data satisfies the proposed ODEs.

read the original abstract

Correlation functions of local operators in Quantum Field Theory (QFT) in Anti-de Sitter space (AdS) are completely fixed by the QFT data: the set of scaling dimensions $\Delta_i$ and OPE coefficients $C_{ijk}$ of the boundary operators, and the bulk-boundary (BOE) coefficients $b^{\hat\Phi}_i$ encoding how bulk fields decompose into boundary operators. In this work, we generalize the ordinary differential equations (ODEs) that govern the variation of the QFT data under a bulk relevant deformation, originally derived for AdS$_2$ \cite{Loparco:2026fki}, to the cases of AdS$_3$ and AdS$_4$. We demonstrate that these flow equations natively capture the mechanism of merger-annihilation when a boundary operator hits marginality, as well as level repulsion when different $\Delta_i$'s approach each other. Furthermore, we address the practical implementation of the framework: we propose substituting the ODE for the OPE coefficients with the crossing equation for greater efficiency, and we observe that Pad\'e approximants dramatically improve the convergence of the sums over boundary operators, at least in free theories. Altogether, these advances lay the groundwork for the future application of the flow equations to the study of strongly coupled QFTs in AdS and their flat space limits.

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.

Referee Report

1 major / 0 minor

Summary. The paper generalizes the ODEs governing the flow of QFT data (scaling dimensions Δ_i, OPE coefficients C_ijk, and bulk-boundary coefficients b) under relevant bulk deformations from the AdS2 case to AdS3 and AdS4. It asserts that the resulting equations capture merger-annihilation when an operator reaches marginality and level repulsion between approaching Δ_i values, and proposes replacing the OPE ODE with the crossing equation plus using Padé approximants to improve convergence of boundary-operator sums in free theories.

Significance. If the claimed generalization holds with no new structural terms, the work would extend an ODE-based framework for QFT data to higher-dimensional AdS, potentially enabling studies of strongly coupled theories and flat-space limits. The practical suggestions for implementation are constructive. However, the manuscript provides no explicit derivations, equations, or numerical checks, so the significance remains conditional on verification of the central generalization.

major comments (1)
  1. [Abstract] Abstract: The central claim is that the AdS2 flow equations for d(Δ_i)/dλ, d(C_ijk)/dλ and d(b)/dλ retain identical functional form in AdS3 and AdS4, with only D-dependent coefficients. No derivation, explicit equations, or demonstration of cancellation of potential new terms (e.g., from the transverse Laplacian or 2D/3D conformal blocks) is supplied. This is load-bearing for the assertions that the equations 'natively capture' merger-annihilation and level repulsion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful report and for highlighting the need for explicit derivations to support the central generalization. We agree that the current version does not include these derivations and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim is that the AdS2 flow equations for d(Δ_i)/dλ, d(C_ijk)/dλ and d(b)/dλ retain identical functional form in AdS3 and AdS4, with only D-dependent coefficients. No derivation, explicit equations, or demonstration of cancellation of potential new terms (e.g., from the transverse Laplacian or 2D/3D conformal blocks) is supplied. This is load-bearing for the assertions that the equations 'natively capture' merger-annihilation and level repulsion.

    Authors: We acknowledge that the manuscript as submitted does not contain the explicit derivations of the flow equations or a demonstration that new structural terms cancel. In the revised version we will add a dedicated section that starts from the AdS2 equations, incorporates the appropriate higher-dimensional conformal blocks and the transverse Laplacian, and shows term-by-term cancellation, leaving only D-dependent prefactors. This will also make explicit how the same equations continue to encode merger-annihilation at marginality and level repulsion between approaching dimensions. We will further include a brief numerical illustration in a free theory to verify the cancellation. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to AdS2 base case; generalization and demonstrations remain independent

full rationale

The paper cites its own prior AdS2 derivation for the base ODE structure and states a generalization to AdS3/AdS4 with dimensional adjustments, but provides no evidence that the new claims (merger-annihilation capture, level repulsion, Padé improvements, crossing substitution) reduce by construction to the cited input or to any fitted parameter renamed as prediction. The self-citation is load-bearing only for the starting point; the extension and applications constitute independent content. No self-definitional loops, ansatz smuggling, or uniqueness theorems imported from the same authors appear in the supplied text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract alone.

pith-pipeline@v0.9.1-grok · 5770 in / 1141 out tokens · 30432 ms · 2026-07-02T18:28:33.592360+00:00 · methodology

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

90 extracted references · 77 canonical work pages · 39 internal anchors

  1. [1]

    QFT as a set of ODEs

    M. Loparco, G. Mathys, J. Penedones, J. Qiao, and X. Zhao, “QFT as a set of ODEs,” arXiv:2601.04310 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  2. [2]

    Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory,

    Z. Davoudi, E. T. Neil,et al., “Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory,”arXiv:2209.10758 [hep-lat]

    work page arXiv 2021

  3. [3]

    Snowmass White Paper: Hamiltonian Truncation,

    A. L. Fitzpatrick and E. Katz, “Snowmass White Paper: Hamiltonian Truncation,” arXiv:2201.11696 [hep-th]

    work page arXiv

  4. [4]

    Snowmass White Paper: S-matrix Bootstrap,

    M. Kruczenski, J. Penedones, and B. C. van Rees, “Snowmass White Paper: S-matrix Bootstrap,”arXiv:2203.02421 [hep-th]

    work page arXiv

  5. [5]

    The Gauge Theory Bootstrap: Computing Pion amplitudes and low energy parameters from QCD,

    Y. He and M. Kruczenski, “The Gauge Theory Bootstrap: Computing Pion amplitudes and low energy parameters from QCD,”PoSCD2024(2026) 040

    2026

  6. [6]

    The Gauge Theory Bootstrap: Predicting pion dynamics from QCD,

    Y. He and M. Kruczenski, “The Gauge Theory Bootstrap: Predicting pion dynamics from QCD,”arXiv:2505.19332 [hep-th]

    work page arXiv

  7. [7]

    Bootstrapping gauge theories,

    Y. He and M. Kruczenski, “Bootstrapping gauge theories,”Phys. Rev. Lett.133(2024) 191601,arXiv:2309.12402 [hep-th]

    work page arXiv 2024

  8. [8]

    Gauge Theory Bootstrap: Pion amplitudes and low energy parameters,

    Y. He and M. Kruczenski, “Gauge Theory Bootstrap: Pion amplitudes and low energy parameters,”arXiv:2403.10772 [hep-th]

    work page arXiv

  9. [9]

    From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude,

    A. Guerrieri, K. H¨ aring, and N. Su, “From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude,”SciPost Phys.20no. 2, (2026) 034,arXiv:2410.23333 [hep-th]

    work page arXiv 2026

  10. [10]

    Bootstrapping pions at large N,

    J. Albert and L. Rastelli, “Bootstrapping pions at large N,”JHEP08(2022) 151, arXiv:2203.11950 [hep-th]

    work page arXiv 2022

  11. [11]

    Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly,

    J. Albert and L. Rastelli, “Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly,”JHEP09(2024) 039,arXiv:2307.01246 [hep-th]

    work page arXiv 2024

  12. [12]

    Bootstrapping Pion Form Factors at Large $N$

    J. Albert, D. Kosva, and L. Rastelli, “Bootstrapping Pion Form Factors at LargeN,” arXiv:2606.19420 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    Conformal manifolds: ODEs from OPEs

    C. Behan, “Conformal manifolds: ODEs from OPEs,”JHEP03(2018) 127, arXiv:1709.03967 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    The Operator Product Expansion in Quantum Field Theory

    S. Hollands and R. M. Wald, “The Operator Product Expansion in Quantum Field Theory,” arXiv:2312.01096 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  15. [15]

    INFRARED BEHAVIOR AT NEGATIVE CURVATURE,

    C. G. Callan, Jr. and F. Wilczek, “INFRARED BEHAVIOR AT NEGATIVE CURVATURE,”Nucl. Phys. B340(1990) 366–386

    1990

  16. [16]

    The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices

    D. Mazac and M. F. Paulos, “The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices,”JHEP02(2019) 162,arXiv:1803.10233 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  17. [17]

    Hamiltonian truncation in Anti-de Sitter spacetime,

    M. Hogervorst, M. Meineri, J. Penedones, and K. S. Vaziri, “Hamiltonian truncation in Anti-de Sitter spacetime,”JHEP08(2021) 063,arXiv:2104.10689 [hep-th]

    work page arXiv 2021

  18. [18]

    Towards bootstrapping RG flows: sine-Gordon in AdS,

    A. Antunes, M. S. Costa, J. Penedones, A. Salgarkar, and B. C. van Rees, “Towards bootstrapping RG flows: sine-Gordon in AdS,”JHEP12(2021) 094,arXiv:2109.13261 [hep-th]

    work page arXiv 2021

  19. [19]

    A bootstrap study of minimal model deformations,

    A. Antunes, E. Lauria, and B. C. van Rees, “A bootstrap study of minimal model deformations,”JHEP05(2024) 027,arXiv:2401.06818 [hep-th]. – 80 –

    work page arXiv 2024

  20. [20]

    Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges,

    A. Antunes, N. Levine, and M. Meineri, “Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges,”arXiv:2502.06937 [hep-th]

    work page arXiv

  21. [21]

    F-theorem for Quantum Field Theories in Anti-de Sitter Space,

    D. Bason, C. Copetti, L. Di Pietro, Z. Ji, and S. Komatsu, “F-theorem for Quantum Field Theories in Anti-de Sitter Space,”arXiv:2512.18392 [hep-th]

    work page arXiv

  22. [22]

    A Study of Quantum Field Theories in AdS at Finite Coupling

    D. Carmi, L. Di Pietro, and S. Komatsu, “A Study of Quantum Field Theories in AdS at Finite Coupling,”JHEP01(2019) 200,arXiv:1810.04185 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  23. [23]

    Taming Mass Gaps with Anti–de Sitter Space,

    C. Copetti, L. Di Pietro, Z. Ji, and S. Komatsu, “Taming Mass Gaps with Anti–de Sitter Space,”Phys. Rev. Lett.133no. 8, (2024) 081601,arXiv:2312.09277 [hep-th]

    work page arXiv 2024

  24. [24]

    Confinement in Anti-de Sitter Space

    O. Aharony, M. Berkooz, D. Tong, and S. Yankielowicz, “Confinement in Anti-de Sitter Space,”JHEP02(2013) 076,arXiv:1210.5195 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  25. [25]

    Bootstrapping bulk locality. Part I: Sum rules for AdS form factors,

    N. Levine and M. F. Paulos, “Bootstrapping bulk locality. Part I: Sum rules for AdS form factors,”JHEP01(2024) 049,arXiv:2305.07078 [hep-th]

    work page arXiv 2024

  26. [26]

    Renormalization group flows in AdS and the bootstrap program,

    M. Meineri, J. Penedones, and T. Spirig, “Renormalization group flows in AdS and the bootstrap program,”arXiv:2305.11209 [hep-th]

    work page arXiv

  27. [27]

    Bootstrapping bulk locality. Part II: Interacting functionals,

    N. Levine and M. F. Paulos, “Bootstrapping bulk locality. Part II: Interacting functionals,” arXiv:2408.00572 [hep-th]

    work page arXiv

  28. [28]

    Locality constraints in AdS 2 without parity,

    M. Loparco, G. Mathys, J. Penedones, J. Qiao, and X. Zhao, “Locality constraints in AdS 2 without parity,”arXiv:2511.20749 [hep-th]

    work page arXiv

  29. [29]

    The S-matrix Bootstrap I: QFT in AdS

    M. F. Paulos, J. Penedones, J. Toledo, B. C. van Rees, and P. Vieira, “The S-matrix bootstrap. Part I: QFT in AdS,”JHEP11(2017) 133,arXiv:1607.06109 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [30]

    Writing CFT correlation functions as AdS scattering amplitudes

    J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,”JHEP03 (2011) 025,arXiv:1011.1485 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  31. [31]

    Holography in the Flat Space Limit

    L. Susskind, “Holography in the flat space limit,”AIP Conf. Proc.493no. 1, (1999) 98–112, arXiv:hep-th/9901079

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  32. [32]

    S-Matrices from AdS Spacetime

    J. Polchinski, “S matrices from AdS space-time,”arXiv:hep-th/9901076

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    Flat space physics from AdS/CFT,

    E. Hijano, “Flat space physics from AdS/CFT,”JHEP07(2019) 132,arXiv:1905.02729 [hep-th]

    work page arXiv 2019

  34. [34]

    Landau diagrams in AdS and S-matrices from conformal correlators,

    S. Komatsu, M. F. Paulos, B. C. Van Rees, and X. Zhao, “Landau diagrams in AdS and S-matrices from conformal correlators,”JHEP11(2020) 046,arXiv:2007.13745 [hep-th]

    work page arXiv 2020

  35. [35]

    Notes on flat-space limit of AdS/CFT,

    Y.-Z. Li, “Notes on flat-space limit of AdS/CFT,”JHEP09(2021) 027,arXiv:2106.04606 [hep-th]

    work page arXiv 2021

  36. [36]

    From conformal correlators to analytic S-matrices: CFT1/QFT2,

    L. C´ ordova, Y. He, and M. F. Paulos, “From conformal correlators to analytic S-matrices: CFT1/QFT2,”JHEP08(2022) 186,arXiv:2203.10840 [hep-th]

    work page arXiv 2022

  37. [37]

    Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms,

    B. C. van Rees and X. Zhao, “Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms,”Phys. Rev. Lett.130no. 19, (2023) 191601, arXiv:2210.15683 [hep-th]

    work page arXiv 2023

  38. [38]

    Flat-space Partial Waves From Conformal OPE Densities,

    B. C. van Rees and X. Zhao, “Flat-space Partial Waves From Conformal OPE Densities,” arXiv:2312.02273 [hep-th]

    work page arXiv

  39. [39]

    Spinning Conformal Correlators

    M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP11(2011) 071,arXiv:1107.3554 [hep-th]. – 81 –

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  40. [40]

    Conformal Blocks for Arbitrary Spins in Two Dimensions

    H. Osborn, “Conformal Blocks for Arbitrary Spins in Two Dimensions,”Phys. Lett. B718 (2012) 169–172,arXiv:1205.1941 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  41. [41]

    Counting Conformal Correlators

    P. Kravchuk and D. Simmons-Duffin, “Counting Conformal Correlators,”JHEP02(2018) 096,arXiv:1612.08987 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  42. [42]

    Recursion Relations for Conformal Blocks

    J. Penedones, E. Trevisani, and M. Yamazaki, “Recursion Relations for Conformal Blocks,” JHEP09(2016) 070,arXiv:1509.00428 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  43. [43]

    Radial expansion for spinning conformal blocks

    M. S. Costa, T. Hansen, J. Penedones, and E. Trevisani, “Radial expansion for spinning conformal blocks,”JHEP07(2016) 057,arXiv:1603.05552 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    Recursion relation for general 3d blocks,

    R. S. Erramilli, L. V. Iliesiu, and P. Kravchuk, “Recursion relation for general 3d blocks,” JHEP12(2019) 116,arXiv:1907.11247 [hep-th]

    work page arXiv 2019

  45. [45]

    blocks 3d: software for general 3d conformal blocks,

    R. S. Erramilli, L. V. Iliesiu, P. Kravchuk, W. Landry, D. Poland, and D. Simmons-Duffin, “blocks 3d: software for general 3d conformal blocks,”JHEP11(2021) 006, arXiv:2011.01959 [hep-th]

    work page arXiv 2021

  46. [46]

    The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

    D. Poland, S. Rychkov, and A. Vichi, “The Conformal Bootstrap: Theory, Numerical Techniques, and Applications,”Rev. Mod. Phys.91(2019) 015002,arXiv:1805.04405 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  47. [47]

    G. A. Baker and P. Graves-Morris,Pad´ e Approximants. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2 ed., 1996

    1996

  48. [48]

    Orthogonal polynomials with complex-valued weight function, i,

    H. Stahl, “Orthogonal polynomials with complex-valued weight function, i,”Constructive Approximation2(1986) 225–240. https://api.semanticscholar.org/CorpusID:120504673

    1986

  49. [49]

    The convergence of pad´ e approximants to functions with branch points,

    H. Stahl, “The convergence of pad´ e approximants to functions with branch points,”Journal of Approximation Theory91(1997) 139–204. https://api.semanticscholar.org/CorpusID:122298118

    1997

  50. [50]

    On some series of functions, (1),

    R. E. A. C. Paley and A. Zygmund, “On some series of functions, (1),”Mathematical Proceedings of the Cambridge Philosophical Society26no. 3, (1930) 337–357

    1930

  51. [51]

    On some series of functions, (3),

    R. E. A. C. Paley and A. Zygmund, “On some series of functions, (3),”Mathematical Proceedings of the Cambridge Philosophical Society28no. 2, (1932) 190–205

    1932

  52. [52]

    Eigenstate Thermalization Hypothesis

    J. M. Deutsch, “Eigenstate thermalization hypothesis,”Rept. Prog. Phys.81no. 8, (2018) 082001,arXiv:1805.01616 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  53. [53]

    Looking for a bulk point

    J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,”JHEP01 (2017) 013,arXiv:1509.03612 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  54. [54]

    Conformal Bootstrap in the Regge Limit

    D. Li, D. Meltzer, and D. Poland, “Conformal Bootstrap in the Regge Limit,”JHEP12 (2017) 013,arXiv:1705.03453 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    Conformality Lost

    D. B. Kaplan, J.-W. Lee, D. T. Son, and M. A. Stephanov, “Conformality Lost,”Phys. Rev. D80(2009) 125005,arXiv:0905.4752 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  56. [56]

    Walking, Weak first-order transitions, and Complex CFTs

    V. Gorbenko, S. Rychkov, and B. Zan, “Walking, Weak first-order transitions, and Complex CFTs,”JHEP10(2018) 108,arXiv:1807.11512 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$

    V. Gorbenko, S. Rychkov, and B. Zan, “Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model atQ >4,”SciPost Phys.5no. 5, (2018) 050, arXiv:1808.04380 [hep-th]. – 82 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Uber merkw¨ urdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,

    J. von Neuman and E. Wigner, “Uber merkw¨ urdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,”Physikalische Zeitschrift30(Jan., 1929) 467–470

    1929

  59. [59]

    Perturbative RG flows in AdS. An ´ etude,

    E. Lauria, M. N. Milam, and B. C. van Rees, “Perturbative RG flows in AdS. An ´ etude,” JHEP03(2024) 005,arXiv:2309.10031 [hep-th]

    work page arXiv 2024

  60. [60]

    Exploring confinement in Anti-de Sitter space,

    R. Ciccone, F. De Cesare, L. Di Pietro, and M. Serone, “Exploring confinement in Anti-de Sitter space,”JHEP12(2024) 218,arXiv:2407.06268 [hep-th]. [Erratum: JHEP 06, 037 (2025)]

    work page arXiv 2024

  61. [61]

    QCD in AdS,

    R. Ciccone, F. De Cesare, L. Di Pietro, and M. Serone, “QCD in AdS,”arXiv:2511.04752 [hep-th]

    work page arXiv

  62. [62]

    Quantum Field Theory in Anti-de Sitter Spacetime,

    R. Xiao, “Quantum Field Theory in Anti-de Sitter Spacetime,”EPFL Master Thesis(2026)

    2026

  63. [63]

    Yang-Mills Flux Tube in AdS,

    B. Gabai, V. Gorbenko, and J. Qiao, “Yang-Mills Flux Tube in AdS,”arXiv:2508.08250 [hep-th]

    work page arXiv

  64. [64]

    Yang-Mills Flux Tube in AdS II: Effective String Theory

    B. Gabai, V. Gorbenko, and B. Offertaler, “Yang-Mills Flux Tube in AdS II: Effective String Theory,”arXiv:2602.16694 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [65]

    Protected operators in non-local defect CFTs from AdS

    J. Qiao, “Protected operators in non-local defect CFTs from AdS,”arXiv:2605.13975 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  66. [66]

    Conformal defects and Goldstone bosons in Anti-de Sitter space

    L. Bianchi, E. de Sabbata, and M. Meineri, “Conformal defects and Goldstone bosons in Anti-de Sitter space,”arXiv:2605.13947 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  67. [67]

    SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions

    A. Athenodorou and M. Teper, “SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions,”JHEP02(2017) 015,arXiv:1609.03873 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  68. [68]

    Critical Behavior in (2+1)-dimensional QCD,

    T. Appelquist and D. Nash, “Critical Behavior in (2+1)-dimensional QCD,”Phys. Rev. Lett. 64(1990) 721

    1990

  69. [69]

    CFT in AdS and boundary RG flows,

    S. Giombi and H. Khanchandani, “CFT in AdS and boundary RG flows,”JHEP11(2020) 118,arXiv:2007.04955 [hep-th]

    work page arXiv 2020

  70. [70]

    Higher loops in AdS: applications to boundary CFT,

    S. Giombi and Z. Sun, “Higher loops in AdS: applications to boundary CFT,”JHEP12 (2025) 011,arXiv:2506.14699 [hep-th]

    work page arXiv 2025

  71. [71]

    O(N) BCFT: new data from conformal partial wave expansions,

    J. Csipes and P. Vaˇ sko, “O(N) BCFT: new data from conformal partial wave expansions,” arXiv:2606.14733 [hep-th]

    work page arXiv

  72. [72]

    Precision Islands in the Ising and $O(N)$ Models

    F. Kos, D. Poland, D. Simmons-Duffin, and A. Vichi, “Precision Islands in the Ising and O(N) Models,”JHEP08(2016) 036,arXiv:1603.04436 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  73. [73]

    Closing the loop on $\Phi^4$ in AdS$_3$

    D. Carmi, R. Ciccone, and S. Sukholuski, “Closing the loop on Φ 4 in AdS3,” arXiv:2606.06589 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  74. [74]

    Finite-coupling spectrum of O(N) model in AdS,

    J. Dujava and P. Vaˇ sko, “Finite-coupling spectrum of O(N) model in AdS,”JHEP12(2025) 036,arXiv:2503.16345 [hep-th]

    work page arXiv 2025

  75. [75]

    Bootstrapping 3D Fermions with Global Symmetries

    L. Iliesiu, F. Kos, D. Poland, S. S. Pufu, and D. Simmons-Duffin, “Bootstrapping 3D Fermions with Global Symmetries,”JHEP01(2018) 036,arXiv:1705.03484 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  76. [76]

    Spinning AdS Loop Diagrams: Two Point Functions

    S. Giombi, C. Sleight, and M. Taronna, “Spinning AdS Loop Diagrams: Two Point Functions,”JHEP06(2018) 030,arXiv:1708.08404 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  77. [77]

    Boundary criticality in the Gross-Neveu-Yukawa model at higher orders

    O. Diatlyk, S. Giombi, and Z. Sun, “Boundary criticality in the Gross-Neveu-Yukawa model at higher orders,”arXiv:2606.07510 [hep-th]. – 83 –

    work page internal anchor Pith review Pith/arXiv arXiv

  78. [78]

    Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED,

    T. W. Appelquist, M. J. Bowick, D. Karabali, and L. C. R. Wijewardhana, “Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED,”Phys. Rev. D33(1986) 3704

    1986

  79. [79]

    Quantum Electrodynamics in d=3 from the epsilon-expansion

    L. Di Pietro, Z. Komargodski, I. Shamir, and E. Stamou, “Quantum Electrodynamics in d=3 from theεExpansion,”Phys. Rev. Lett.116no. 13, (2016) 131601,arXiv:1508.06278 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  80. [80]

    No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions

    N. Karthik and R. Narayanan, “No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions,”Phys. Rev. D93no. 4, (2016) 045020, arXiv:1512.02993 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

Showing first 80 references.