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't Hooft loops in N=4 super-Yang-Mills

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Quantizing around the monopole turns 't Hooft loop correlators into flower-diagram combinatorics that match exact results.

desk verdict Solid paper with a strong all-orders fishnet result; the flower-diagram one-point story is a well-flagged conjecture, not a proof. read the letter →

arxiv 2412.01972 v2 pith:DDYCT7SV submitted 2024-12-02 hep-th

Charlotte Kristjansen , Konstantin Zarembo This is my paper · ORCID
classification hep-th
keywords 'tHooftloopN=4super-Yang-Millsmonopolebackgroundfieldquantizationchiralprimaryone-pointfunctionsflowerdiagramsWilsonfishnetlimitholographicstrongcoupling
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

The paper builds a perturbative framework for the 't Hooft line in N=4 super-Yang-Mills, treating the Dirac-monopole field as a classical background and quantizing the fluctuations around it. Within that framework, one-point functions of chiral primaries are claimed to be saturated, up to wrapping order, by 'flower' diagrams — graphs with no interaction vertices — whose zero-dimensional combinatorial resummation reproduces the planar-exact localization results through Chebyshev polynomials. The same background-field methods give the correlator of a parallel supersymmetric Wilson line with the 't Hooft line, and in the fishnet limit the ladder diagrams resum to the closed charge formula α = (q cos φ / 2)(1 + √(1 + λ/(4π²q²))). At strong coupling this formula tends to √λ cos φ/(4π), in precise agreement with the string-theory minimal-surface computation of the quark–monopole potential. If correct, the paper turns a disorder operator that standard perturbation theory struggles with into a systematically quantizable object whose output connects localization, integrability, and holography.

What carries the argument

The load-bearing object is the anomalous propagator G_− = G̃ − G, the difference between the hard and easy scalar Green's functions in the monopole background. It vanishes as q → 0, is UV finite at coincident points, and in collinear kinematics telescopes to the lowest partial wave j = q — a 'Kondo effect' that reduces the defect dynamics to AdS2. The other central devices are the zero-dimensional Gaussian model Z = [[1, φ†],[φ, 0]], whose Feynman rules generate the flower diagrams and whose recursion Q_{L+1} = Q_L + ξQ_{L−1} is solved by Chebyshev polynomials; and the Dyson equation for the Wilson–'t Hooft correlator, whose Laplace image is algebraic and, in the limit cosφ → ∞, yields the closed formula (4.34). The fluctuation spectrum itself is organized by the monopole-shifted angular momentum ℓ = q, q+1, ... and by the vector and spinor monopole harmonics, which give the remarkably simple mode indices ν = j − 1/2, j + 1/2, j + 1/2, j + 3/2.

What would settle it

Compute the three-loop ($λ^{3}$) contribution to the one-point function of tr $Z^{3}$ in the monopole background: the crucial cancellation requires the sum of self-energy and triple-vertex diagrams to vanish, and any non-zero result at this order would falsify the flower-diagram saturation and the claimed match with the planar-exact formula (3.16).

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that the supersymmetric 't Hooft line admits a complete background-field quantization, and that this quantization makes previously intractable correlators exactly resummable. The scalar Green's functions split into easy and hard sectors; their difference, the anomalous propagator G_−, is what survives in physical observables, and in collinear kinematics its partial-wave tower collapses to a single lowest harmonic — the 'Kondo effect' that converts the defect problem into an effective one-dimensional theory. For chiral primaries tr Z^L, the claim is that flower diagrams (no interaction vertices) saturate the one-point function up to wrapping corrections of order λ^L: the zero-dimensional Gaussian average over a matrix Z = [[1, φ†],[φ, 0]] produces C_L = 2T_L(u)/(i^L√L) with u = 2πiq/√λ, matching the planar-exact localization formula for odd L fully and for even L up to the wrapping gap. For the Wilson–'t Hooft correlator, a Dyson equation whose kernel is G_− is solved by Laplace transform, and in the fishnet double-scaling limit the effective Coulomb charge becomes α = (q cosφ/2)(1 + √(1 + λ/(4π²q²))); at strong coupling this approaches √λ cosφ/(4π), which the holographic minimal-surface solution reproduces with the same numerical coefficient.

Load-bearing premise

The load-bearing premise is that the two-loop cancellation between self-energy and triple-vertex diagrams continues to all loop orders, so that chiral-primary one-point functions are saturated by flower diagrams; a secondary fragile step is assuming the large-N localization formula derived for q=1/2 holds for arbitrary q.

Editorial extensions

If this is right

  • Odd-length chiral primaries acquire one-point functions that are finite polynomials in the 't Hooft coupling, with the perturbative series truncating at order λ^{(L−1)/2}; even-length ones show a gap between order λ^{L/2} and the wrapping order λ^L.
  • The flower-diagram sum matches the planar-exact localization expression for all L up to wrapping order, so the Chebyshev parametrization of the localization result is given a Feynman-diagram interpretation.
  • In the fishnet limit, the Wilson–'t Hooft Coulomb charge is α = (q cosφ/2)(1 + √(1 + λ/(4π²q²))), and at strong coupling this tends to √λ cosφ/(4π), independent of q, exactly as the holographic minimal-surface computation requires.
  • The minimal-charge Wilson–'t Hooft correlator inherits the radius of convergence λ_c = π² shared by other integrable or localizable observables, because the resummed α coincides with the giant-magnon energy at the Brillouin zone edge.
  • The supersymmetric monopole background supports no fermion zero modes, the Callan–Rubakov effect is absent, and the one-loop Konishi one-point function is explicitly finite (for q=1/2, ⟨K⟩_T = (π²/√3 λ r^{Δ_K})[1 + (λ/4π²)(5 − 9 ln 2)]).

Reading between the lines

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

  • The same flower-diagram/Chebyshev mechanism may underlie one-point functions of other supersymmetric defects with Kondo-like truncation, such as the D3-D5 domain wall; the paper itself notes the parallel but does not prove a universal statement.
  • If the two-loop self-energy/triple-vertex cancellation is a consequence of the underlying osp(4*|4) supermultiplet structure, analogous cancellations should appear in supersymmetric monopole operators in ABJM theory, where the paper suggests similar simplifications.
  • The strong-coupling independence of α on q suggests that finite-q corrections to the holographic computation would provide a sharp test of the fishnet resummation beyond the leading saddle point.
  • A direct numerical or bootstrap computation of the Wilson–'t Hooft correlator at intermediate coupling could test whether the fishnet formula (4.34) is the leading term of a larger analytic structure controlled by the conjectured scaling α = cosφ α̂(λ cosφ) near φ = π/2.
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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

3 major / 4 minor

Summary. The paper develops a background-field quantization of the supersymmetric 't Hooft line in planar N=4 super-Yang-Mills, constructs the relevant scalar, vector, and fermion propagators in the monopole background, and applies this formalism to two classes of observables. The first application is the one-point functions of chiral primary operators: the authors show that the sum of 'flower' diagrams reproduces the planar-exact localization result (3.16) up to wrapping order, and exactly for odd-length operators, and they connect this to a truncation/gap structure in the perturbative series. They also compute the one-loop one-point function of the Konishi operator and set up a general spin-chain overlap formalism for non-protected operators. The second application is the Wilson-'t Hooft correlator: after a one-loop computation, the paper defines a fishnet-like limit and resums the ladder diagrams through a Dyson equation, obtaining the closed-form effective charge (4.34), which matches a string-theory computation at strong coupling. The paper is transparent about two conjectural inputs: the all-order persistence of the flower-diagram saturation and the continuation of the localization formula (3.7) to arbitrary monopole charge.

Significance. If the two conjectural inputs are correct, the paper provides substantial new evidence for a surprising structural property of 't Hooft-line defects: quantum corrections to chiral-primary one-point functions are saturated by simple non-interacting diagrams up to wrapping order, with a Kondo-like truncation to low partial waves. The Wilson-'t Hooft fishnet resummation and its strong-coupling match with string theory are also impressive and give a concrete, falsifiable prediction for the effective Coulomb charge. The manuscript is explicit and self-critical about its assumptions; the algebraic steps are mostly spelled out, and the final formulas are checked against independently known localization and string results rather than fitted parameters. The main limitations are that the all-loop cancellation assumption in Section 3.1.2 is not proven, and that the arbitrary-q extension of (3.7) is explicitly conjectural. These issues do not undermine the q=1/2 case, but they do affect the paper's stated scope of arbitrary monopole charge.

major comments (3)
  1. [Section 3.1.2, after Eq. (3.19)] The central claim that Eq. (3.34) reproduces the planar-exact localization result (3.16) up to wrapping order rests on the 'crucial assumption' that the two-loop cancellation between self-energy and induced triple-vertex diagrams persists to all higher orders. The argument given, namely that the combinatorics is independent of the operator length L, only shows that the two-loop cancellation found for L=3 extends to other values of L at the same loop order; it says nothing about three and higher loops. This is load-bearing because localization predicts exact zeros in specific higher-order coefficients, for example all coefficients beyond O(λ) in C_3. A single non-vanishing three-loop non-flower diagram would invalidate the identification of the flower sum with the full result. I ask the authors to either provide an all-orders argument for the persistence of the cancellation, or to perform an explicit three-loop check for a small L, or to state more precisely that Eq. (3.34) is only a conjectured partial resummation.
  2. [Section 3.1.1, Eq. (3.7)] Equation (3.7) is the planar-exact OPE coefficient used as the benchmark for the flower-diagram sum, and the paper explicitly states that its derivation is valid only for q=1/2. The subsequent formulas (3.8)-(3.12), and the claimed agreement for arbitrary q, therefore depend on the unproven conjecture that the same expression continues to hold for all half-integer q. This does not affect the minimal q=1/2 case, which is the physically elementary monopole, but it is a separate load-bearing assumption for the arbitrary-q claims made in Sections 3.1.1 and 3.1.2. The paper acknowledges this gap, but as it stands the 'match' for q>1/2 is conditional on a conjecture rather than a derivation.
  3. [Section 4.2, Eq. (4.32)-(4.34)] The fishnet-limit resummation leading to Eq. (4.34) assumes that ladder diagrams dominate in the double-scaling limit φ→i∞. The two-loop power-counting discussion in Section 4.2.1 identifies the ladder topology as the leading one at that order, but no all-orders argument is given that all non-ladder diagrams are suppressed uniformly in cos φ at every loop order. Since Eq. (4.34) is presented as a fully resummed, non-perturbative result, this all-orders dominance is load-bearing. The agreement with the string-theory computation is encouraging, but a systematic all-orders power-counting or an explicit subleading-diagram estimate would be needed to put the resummation on firmer ground.
minor comments (4)
  1. [Section 1, paragraph 2] There is a typo: 'see see e.g.' should read 'see e.g.'.
  2. [Section 3.1.3, paragraph 6] The phrase 'this was taken was taken care of by dimensional regularization' contains a duplicated 'was taken'; it should read 'this was taken care of by dimensional regularization'.
  3. [Section 2.7, Eqs. (2.105)-(2.108)] The summation formulas for the spinor monopole harmonics are said to be supported only by a numerical investigation. Since these formulas are presented as part of the framework and are intended for future fermion propagator constructions, it would be preferable to either prove them or explicitly mark them as numerically verified conjectures.
  4. [Section 4.2.2, Eq. (4.33)] In the passage from Eq. (4.32) to Eq. (4.33), the paper uses the large-argument asymptotic (4.18) for f_ν and then solves for α. It may be useful to state explicitly that this is a double limit: first cos φ → ∞ with α ∼ q cos φ, then Eq. (4.33) is solved for α. This would clarify the order of limits and the meaning of 'fully non-perturbative' in this context.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's perturbative derivations are checked against independent localization and string-theory results, not fitted to them.

full rationale

The paper's central derivation chain is self-contained rather than circular. The one-point function result (3.34) is obtained by explicitly resumming flower diagrams in a zero-dimensional Gaussian model whose propagator is fixed by the anomalous Green's function (2.67) and the normalization convention (3.17); the rapidity u emerges from the Gaussian average as u = 2πiq/√λ in (3.33), which is the same quantization condition as in the localization formula, but it is not a fitted parameter and the equality is a computed coincidence. The exact benchmark (3.7) is cited from the authors' prior work [8], but that work is an independent localization/S-duality result and is used as a comparison target, not as an input that forces the diagrammatic answer. The 'crucial assumption' in Section 3.1.2 that two-loop self-energy/triple-vertex cancellations persist to all orders is explicitly flagged as an unproven conjecture; a conjecture of this kind is a substantive dynamical assumption that could in principle fail, which is a correctness risk rather than circularity. The Wilson-'t Hooft fishnet result (4.34) is derived by solving the Dyson equation (4.23) and then matched to an independent string-theory computation (4.35)-(4.42), again with no parameter fitted to the final answer. The q > 1/2 continuation of (3.7) is also explicitly presented as a conjecture and does not affect the minimal q = 1/2 case. Self-citations to [8,9] supply benchmarks or future checks, not the conclusions themselves, so they do not constitute load-bearing circularity.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central results do not introduce new physical entities or fit free parameters; they rely on known monopole harmonic analysis, supersymmetry of N=4 SYM, and several explicitly flagged assumptions (arbitrary-q continuation, persistent cancellations, ladder dominance).

assumptions (6)
  • domain assumption The classical monopole background cannot receive quantum corrections: conformal symmetry fixes the radial form, Dirac quantization forbids renormalization of q, and supersymmetry ties the scalar to the magnetic field.
    Section 2, page 3, used to justify treating (2.1),(2.2) as a fixed background and to interpret the perturbative expansion.
  • domain assumption Dimensional regularization of the 't Hooft line as a (d-3)-dimensional monopole sheet preserves the quantized flux and the AdS_{d-2} x S^2 conformal structure.
    Section 2.4, pages 9-10; needed to define UV-finite propagators and to perform partial-wave sums before taking d to 4.
  • ad hoc to paper The planar-exact OPE coefficient (3.7), derived for q=1/2, continues to hold for arbitrary monopole charge.
    Section 3.1.1, page 26 explicitly says 'We assume nevertheless that the large-N formula continues to hold for arbitrary q'.
  • ad hoc to paper The two-loop cancellation between self-energy and triple-vertex diagrams persists to all loop orders.
    Section 3.1.2, page 29: 'We now make a crucial assumption... that cancellations just observed persist to higher loops.' This is needed for flower diagrams to saturate chiral-primary one-point functions.
  • ad hoc to paper In the fishnet limit phi goes to i*infinity with lambda fixed, ladder-type diagrams dominate the Wilson-'t Hooft correlator.
    Section 4.2.1, pages 45-46; power counting of two-loop topologies is used to argue only iterated one-loop diagrams survive, but this is not proven to all orders.
  • domain assumption The holographic dual of the minimal 't Hooft line is an infinitely heavy planar D1-brane, and the string worldsheet meets it at right angles.
    Section 4.3, pages 49-50; needed for the method-of-images construction of the minimal surface and the strong-coupling match.

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Cite this review

Pith. "Pith review of 't Hooft loops in N=4 super-Yang-Mills." pith.science (2026). https://pith.science/paper/DDYCT7SV

@misc{pith2026241201972,
  author       = {Pith},
  title        = {Pith review of: 't Hooft loops in N=4 super-Yang-Mills},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DDYCT7SV}},
  note         = {Machine review of arXiv:2412.01972}
}
read the original abstract

We set up a perturbative framework for the 't Hooft line in the N=4 super-Yang-Mills theory, and apply it to correlators thereof with Wilson loops and local operators. Using this formalism we obtain a number of perturbative and non-perturbative results that directly connect to localization, holography and integrability.

Figures

Figures reproduced from arXiv: 2412.01972 by the authors.

Figure 1
Figure 1. The tadpole diagram. D∆(1) = Γ(2 − d 2 )Γ(∆) (4π) d 2 −1Γ(∆ − d + 4) . (2.39) The dimensionally-regularized tadpole thus equals to tadpole ≡ G(x, x) = Γ(2 − d 2 ) (4π) d 2 r d−2 ∞ ∑ j=q (2j + 1) Γ(j + d 2 − 1) Γ(j − d 2 + 3) . (2.40) There is an obvious 1/ε pole at d → 4, but this is not the only source of infinities. Setting d = 4 results in a divergent sum over partial waves ∑j (2j + 1). It may be tempting to zeta… view at source ↗
Figure 2
Figure 2. Perturbative expansion for (a) trZ 2 , (b) trZ 3 . Wrapping corrections are blue-colored. The diagrams in green mutually cancel. 3.1.2 Flower diagrams An expectation value of trZL can be computed order-by-order in λ by ex￾panding the constituent field around the classical background: Z = q/r + z, and computing the ensuing correlators of z evaluated at coincident points. The real and imaginary parts of z = ϕ1 + iϕ2 a… view at source ↗
Figure 3
Figure 3. A flower diagram. symmetry reason for the propagator of z to be protected. What is surprising is that cancellations do occur in ⟨trZ3 ⟩T : the perturbative series in (3.9) truncate at O(λ) and thus the complete two-loop correction must vanish. When expressed in diagrams, this means that the triple-vertex contribution6 (fig. 2b) completely compensates the self-energy propagator diagrams. It is easy to see that the co… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The one-loop correction to the Wilson-’t Hooft correlator. [PITH_FULL_IMAGE:figures/full_fig_p043_4.png]
Figure 5
Figure 5. Figure 5: Two-loop diagram topologies. The summation over the color indices [PITH_FULL_IMAGE:figures/full_fig_p046_5.png]
Figure 6
Figure 6. Figure 6: Pictorial form of the Dyson equation (4.23). Its iterative solution gen [PITH_FULL_IMAGE:figures/full_fig_p047_6.png]
Figure 7
Figure 7. Figure 7: The minimal surface describing the correlator of Wilson and ’t Hooft [PITH_FULL_IMAGE:figures/full_fig_p051_7.png]
Figure 8
Figure 8. Figure 8: The Coulomb charge at strong coupling, as a function of the R-symmetry [PITH_FULL_IMAGE:figures/full_fig_p052_8.png]

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

77 extracted references · 22 canonical work pages · cited by 5 Pith papers

  1. [1]

    Localization techniques in quantum field theories

    V. Pestun et al., “Localization techniques in quantum field theories” , J. Phys. A 50, 440301 (2017), 1608.02952. • P. Liendo, L. Rastelli and B. C. van Rees, “The Bootstrap Program for Boundary CFT d”, JHEP 1307, 113 (2013), 1210.4258. • C. Kristjansen and K. Zarembo, “Integrable Holographic Defect CFTs”, 2401.17144

    arXiv 2017

  2. [2]

    Wilson loops in N = 4 supersymmetric Yang-Mills theory

    J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in N = 4 supersymmetric Yang-Mills theory”, Nucl. Phys. B582, 155 (2000), hep-th/0003055

    arXiv 2000

  3. [3]

    One-loop one-point functions in gauge-gravity dualities with defects

    I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen and M. Wilhelm, “One-loop one-point functions in gauge-gravity dualities with defects”, Phys. Rev. Lett. 117, 231603 (2016), 1606.01886

    arXiv 2016

  4. [4]

    A Quantum Check of AdS/dCFT

    I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen and M. Wilhelm, “A Quantum Check of AdS/dCFT” , JHEP 1701, 098 (2017), 1611.04603

    arXiv 2017

  5. [5]

    A Quantum Check of Non-Supersymmetric AdS/dCFT

    A. Gimenez Grau, C. Kristjansen, M. Volk and M. Wilhelm, “A Quantum Check of Non-Supersymmetric AdS/dCFT” , JHEP 1901, 007 (2019), 1810.11463. • A. Gimenez-Grau, C. Kristjansen, M. Volk and M. Wilhelm, “A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on S4”, JHEP 2004, 132 (2020), 1912.02468

    arXiv 2019

  6. [6]

    Surface operators and exact holography

    C. Choi, J. Gomis and R. I. Garc ´ ıa,“Surface operators and exact holography”, JHEP 2412, 195 (2024), 2406.08541

    arXiv 2024

  7. [7]

    Integrable Conformal Defects in N=4 SYM

    M. de Leeuw and A. Holguin, “Integrable Conformal Defects in N=4 SYM” , 2406.13741

    arXiv

  8. [8]

    ’t Hooft loops and integrability

    C. Kristjansen and K. Zarembo, “’t Hooft loops and integrability” , JHEP 2308, 184 (2023), 2305.03649

    arXiv 2023

Show all 77 references
  1. [9]

    Dual overlaps and finite coupling ’t Hooft loops

    T. Gombor and Z. Bajnok, “Dual overlaps and finite coupling ’t Hooft loops”, JHEP 2412, 034 (2024), 2408.14901. 54

    2024 arXiv

  2. [10]

    A new solution to the Callan Rubakov effect

    T. D. Brennan, “A new solution to the Callan Rubakov effect” , JHEP 2411, 170 (2024), 2309.00680

    2024 arXiv

  3. [11]

    Monopoles, Scattering, and Generalized Symmetries

    M. van Beest, P. Boyle Smith, D. Delmastro, Z. Komargodski and D. Tong, “Monopoles, Scattering, and Generalized Symmetries” , 2306.07318

    arXiv

  4. [12]

    Fermion-monopole scattering in the Standard Model

    M. van Beest, P. Boyle Smith, D. Delmastro, R. Mouland and D. Tong, “Fermion-monopole scattering in the Standard Model” , JHEP 2408, 004 (2024), 2312.17746

    2024 arXiv

  5. [13]

    Scattering amplitudes of fermions on monopoles

    V. V. Khoze, “Scattering amplitudes of fermions on monopoles” , JHEP 2311, 214 (2023), 2308.09401

    2023 arXiv

  6. [14]

    Asymptotic One-Point Functions in Gauge-String Duality with Defects

    I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen and M. Wilhelm, “Asymptotic One-Point Functions in Gauge-String Duality with Defects”, Phys. Rev. Lett. 119, 261604 (2017), 1704.07386

    2017 arXiv

  7. [15]

    New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N = 4 Supersymmetric Yang-Mills Theory

    ¨O. G¨ urdo˘ gan and V. Kazakov,“New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N = 4 Supersymmetric Yang-Mills Theory” , Phys. Rev. Lett. 117, 201602 (2016), 1512.06704

    2016 arXiv

  8. [16]

    Quark - monopole potentials in large N superYang-Mills

    J. A. Minahan, “Quark - monopole potentials in large N superYang-Mills” , Adv. Theor. Math. Phys. 2, 559 (1998), hep-th/9803111

    1998 arXiv

  9. [17]

    Correlator of Wilson and t’Hooft Loops at Strong Coupling in N=4 SYM Theory

    A. Gorsky, A. Monin and A. V. Zayakin, “Correlator of Wilson and t’Hooft Loops at Strong Coupling in N=4 SYM Theory” , Phys. Lett. B 679, 529 (2009), 0904.3665

    2009 arXiv

  10. [18]

    On the Phase Transition Towards Permanent Quark Confinement

    G. ’t Hooft, “On the Phase Transition Towards Permanent Quark Confinement”, Nucl. Phys. B 138, 1 (1978)

    1978

  11. [19]

    Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality

    A. Kapustin, “Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality” , Phys. Rev. D74, 025005 (2006), hep-th/0501015

    2006 arXiv

  12. [20]

    Quantised singularities in the electromagnetic field,

    P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” , Proc. Roy. Soc. Lond. A 133, 60 (1931)

    1931

  13. [21]

    Monopoles, Dirac Strings and Generalised Symmetries

    C. M. Hull, “Monopoles, Dirac Strings and Generalised Symmetries” , 2411.18741

    arXiv

  14. [22]

    Supersymmetric Yang-Mills Theories

    L. Brink, J. H. Schwarz and J. Scherk, “Supersymmetric Yang-Mills Theories”, Nucl.Phys. B121, 77 (1977)

    1977

  15. [23]

    Gamma matrices, Majorana fermions, and discrete symmetries in Minkowski and Euclidean signature

    M. Stone, “Gamma matrices, Majorana fermions, and discrete symmetries in Minkowski and Euclidean signature” , J. Phys. A 55, 205401 (2022), 2009.00518

    2022 arXiv

  16. [24]

    Diagonalization of the Kondo Hamiltonian

    N. Andrei, “Diagonalization of the Kondo Hamiltonian” , Phys. Rev. Lett. 45, 379 (1980). • P. Wiegmann, “Exact solution of sd 55 exchange model at T= 0” , JETP Lett. 31, 364 (1980). • P. Wiegmann, “Exact solution of the sd exchange model (Kondo problem)” , J. Phys. C 14, 1463 (1981)

    1980

  17. [25]

    Die verallgemeinerten Kugelfunktionen und die Wellenfunktionen eines Elektrons im Felde eines Magnetpoles

    I. Tamm, “Die verallgemeinerten Kugelfunktionen und die Wellenfunktionen eines Elektrons im Felde eines Magnetpoles” , Z. Phys. 71, 141 (1931)

    1931

  18. [26]

    Zur Theorie magnetisch geladener Teilchen

    M. Fierz, “Zur Theorie magnetisch geladener Teilchen” , Helvetica Physica Acta 17, 27 (1944)

    1944

  19. [27]

    Dirac’s Monopole Without Strings: Classical Lagrangian Theory

    T. T. Wu and C. N. Yang, “Dirac’s Monopole Without Strings: Classical Lagrangian Theory”, Phys. Rev. D 14, 437 (1976)

    1976

  20. [28]

    Magnetic Flux, Angular Momentum, and Statistics

    F. Wilczek, “Magnetic Flux, Angular Momentum, and Statistics” , Phys. Rev. Lett. 48, 1144 (1982)

    1982

  21. [29]

    Some Properties of Monopole Harmonics

    T. T. Wu and C. N. Yang, “Some Properties of Monopole Harmonics” , Phys. Rev. D 16, 1018 (1977)

    1977

  22. [30]

    Monopole vector spherical harmonics

    E. J. Weinberg, “Monopole vector spherical harmonics” , Phys. Rev. D 49, 1086 (1994), hep-th/9308054

    1994 arXiv

  23. [31]

    Scattering of a Dirac Particle with Charge Ze by a Fixed Magnetic Monopole

    Y. Kazama, C. N. Yang and A. S. Goldhaber, “Scattering of a Dirac Particle with Charge Ze by a Fixed Magnetic Monopole” , Phys. Rev. D 15, 2287 (1977)

    1977

  24. [32]

    On the Existence of Bound States for a Massive Spin 1 Particle and a Magnetic Monopole

    H. A. Olsen, P. Osland and T. T. Wu, “On the Existence of Bound States for a Massive Spin 1 Particle and a Magnetic Monopole” , Phys. Rev. D 42, 665 (1990)

    1990

  25. [33]

    Superheavy Magnetic Monopoles and Proton Decay

    V. A. Rubakov, “Superheavy Magnetic Monopoles and Proton Decay” , JETP Lett. 33, 644 (1981). • C. G. Callan, Jr., “Disappearing Dyons”, Phys. Rev. D 25, 2141 (1982). • V. A. Rubakov, “Adler-Bell-Jackiw Anomaly and Fermion Number Breaking in the Presence of a Magnetic Monopole”...

    1981

  26. [34]

    Callan-Rubakov effect and higher charge monopoles

    T. D. Brennan, “Callan-Rubakov effect and higher charge monopoles” , JHEP 2302, 159 (2023), 2109.11207

    2023 arXiv

  27. [35]

    Phases of Wilson lines: conformality and screening

    O. Aharony, G. Cuomo, Z. Komargodski, M. Mezei and A. Raviv-Moshe, “Phases of Wilson lines: conformality and screening” , JHEP 2312, 183 (2023), 2310.00045

    2023 arXiv

  28. [36]

    Summation formulae for spherical spinors

    A. Bechler, “Summation formulae for spherical spinors” , J. Phys. A: Math. Gen. 26, 6039 (1993). 56

    1993

  29. [37]

    More exact predictions of SUSYM for string theory

    G. W. Semenoff and K. Zarembo, “More exact predictions of SUSYM for string theory”, Nucl. Phys. B616, 34 (2001), hep-th/0106015

    2001 arXiv

  30. [38]

    Wilson loops in N = 4 SYM and fermion droplets

    K. Okuyama and G. W. Semenoff, “Wilson loops in N = 4 SYM and fermion droplets”, JHEP 0606, 057 (2006), hep-th/0604209

    2006 arXiv

  31. [39]

    Exact Results for ’t Hooft Loops in Gauge Theories on S4

    J. Gomis, T. Okuda and V. Pestun, “Exact Results for ’t Hooft Loops in Gauge Theories on S4”, JHEP 1205, 141 (2012), 1105.2568

    2012 arXiv

  32. [40]

    Quantum ’t Hooft operators and S-duality in N=4 super Yang-Mills

    J. Gomis, T. Okuda and D. Trancanelli, “Quantum ’t Hooft operators and S-duality in N=4 super Yang-Mills” , Adv.Theor.Math.Phys. 13, 1941 (2009), 0904.4486. • J. Gomis and T. Okuda, “S-duality, ’t Hooft operators and the operator product expansion”, JHEP 0909, 072 (2009), 0906.3011

    2009 arXiv

  33. [41]

    Gauge Theory, Ramification, And The Geometric Langlands Program

    S. Gukov and E. Witten, “Gauge Theory, Ramification, And The Geometric Langlands Program”, hep-th/0612073

    arXiv

  34. [42]

    Probing N=4 SYM With Surface Operators

    N. Drukker, J. Gomis and S. Matsuura, “Probing N=4 SYM With Surface Operators”, JHEP 0810, 048 (2008), 0805.4199

    2008 arXiv

  35. [43]

    An exact prediction of N = 4 SUSYM theory for string theory

    N. Drukker and D. J. Gross, “An exact prediction of N = 4 SUSYM theory for string theory” , J. Math. Phys. 42, 2896 (2001), hep-th/0010274

    2001 arXiv

  36. [44]

    Long-range P SU(2, 2∣4) Bethe ansaetze for gauge theory and strings

    N. Beisert and M. Staudacher, “Long-range P SU(2, 2∣4) Bethe ansaetze for gauge theory and strings” , Nucl. Phys. B727, 1 (2005), hep-th/0504190

    2005 arXiv

  37. [45]

    Quantum Spectral Curve for Planar N = Super-Yang-Mills Theory

    N. Gromov, V. Kazakov, S. Leurent and D. Volin, “Quantum Spectral Curve for Planar N = Super-Yang-Mills Theory”, Phys. Rev. Lett. 112, 011602 (2014), 1305.1939

    2014 arXiv

  38. [46]

    The Noncommutative bion core

    N. R. Constable, R. C. Myers and O. Tafjord, “The Noncommutative bion core”, Phys.Rev. D61, 106009 (2000), hep-th/9911136

    2000 arXiv

  39. [47]

    Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

    M. de Leeuw, A. C. Ipsen, C. Kristjansen, K. E. Vardinghus and M. Wilhelm, “Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations”, JHEP 1708, 020 (2017), 1705.03898

    2017 arXiv

  40. [48]

    Integrable boundary states in D3-D5 dCFT: beyond scalars

    C. Kristjansen, D. M¨ uller and K. Zarembo, “Integrable boundary states in D3-D5 dCFT: beyond scalars” , JHEP 2008, 103 (2020), 2005.01392

    2020 arXiv

  41. [49]

    Holography and defect conformal field theories

    O. DeWolfe, D. Z. Freedman and H. Ooguri, “Holography and defect conformal field theories” , Phys.Rev. D66, 025009 (2002), hep-th/0111135

    2002 arXiv

  42. [50]

    Open and closed string interpretation of SUSY CFT’s on branes with boundaries

    A. Karch and L. Randall, “Open and closed string interpretation of SUSY CFT’s on branes with boundaries” , JHEP 0106, 063 (2001), hep-th/0105132

    2001 arXiv

  43. [51]

    Expectation values of chiral primary operators in holographic interface CFT

    K. Nagasaki and S. Yamaguchi, “Expectation values of chiral primary operators in holographic interface CFT” , Phys.Rev. D86, 086004 (2012), 1205.1674. 57

    2012 arXiv

  44. [52]

    D-branes, monopoles and Nahm equations

    D.-E. Diaconescu, “D-branes, monopoles and Nahm equations” , Nucl.Phys. B503, 220 (1997), hep-th/9608163

    1997 arXiv

  45. [53]

    One-point Functions in Defect CFT and Integrability

    M. de Leeuw, C. Kristjansen and K. Zarembo, “One-point Functions in Defect CFT and Integrability” , JHEP 1508, 098 (2015), 1506.06958. • I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen and K. Zarembo, “One-point Functions in AdS/dCFT from Matrix Product States” , JHEP 1602, 052...

    2015 arXiv

  46. [54]

    Non-perturbative defect one-point functions in planar N = 4 super-Yang-Mills

    S. Komatsu and Y. Wang, “Non-perturbative defect one-point functions in planar N = 4 super-Yang-Mills”, Nucl. Phys. B 958, 115120 (2020), 2004.09514

    2020 arXiv

  47. [55]

    The Dilatation operator of N=4 super Yang-Mills theory and integrability

    N. Beisert, “The Dilatation operator of N=4 super Yang-Mills theory and integrability”, Phys. Rept. 405, 1 (2004), hep-th/0407277

    2004 arXiv

  48. [56]

    Vacuum Condensates on the Coulomb Branch

    V. Ivanovskiy, S. Komatsu, V. Mishnyakov, N. Terziev, N. Zaigraev and K. Zarembo, “Vacuum Condensates on the Coulomb Branch” , 2405.19043

    arXiv

  49. [57]

    The Bethe-ansatz for N = 4 super Yang-Mills

    J. A. Minahan and K. Zarembo, “The Bethe-ansatz for N = 4 super Yang-Mills”, JHEP 0303, 013 (2003), hep-th/0212208

    2003 arXiv

  50. [58]

    The cusp anomalous dimension at three loops and beyond

    D. Correa, J. Henn, J. Maldacena and A. Sever, “The cusp anomalous dimension at three loops and beyond” , JHEP 1205, 098 (2012), 1203.1019

    2012 arXiv

  51. [59]

    Ladder Limit for Correlators of Wilson Loops

    D. H. Correa, P. Pisani and A. Rios Fukelman, “Ladder Limit for Correlators of Wilson Loops” , JHEP 1805, 168 (2018), 1803.02153

    2018 arXiv

  52. [60]

    Static potential in N=4 supersymmetric Yang-Mills theory

    J. Erickson, G. Semenoff, R. Szabo and K. Zarembo, “Static potential in N=4 supersymmetric Yang-Mills theory” , Phys.Rev. D61, 105006 (2000), hep-th/9911088

    2000 arXiv

  53. [61]

    Dynamics of flux tubes in large N gauge theories

    I. R. Klebanov, J. M. Maldacena and C. B. Thorn, “Dynamics of flux tubes in large N gauge theories” , JHEP 0604, 024 (2006), hep-th/0602255

    2006 arXiv

  54. [62]

    Ladders for Wilson Loops Beyond Leading Order

    D. Bykov and K. Zarembo, “Ladders for Wilson Loops Beyond Leading Order”, JHEP 1209, 057 (2012), 1206.7117

    2012 arXiv

  55. [63]

    Quark-anti-quark potential in N = 4 SYM

    N. Gromov and F. Levkovich-Maslyuk, “Quark-anti-quark potential in N = 4 SYM” , JHEP 1612, 122 (2016), 1601.05679

    2016 arXiv

  56. [64]

    The ground state of long-range Schr¨ odinger equations and staticqq potential

    M. Beccaria, G. Metafune and D. Pallara, “The ground state of long-range Schr¨ odinger equations and staticqq potential”, JHEP 1605, 040 (2016), 1603.03596. • M. Beccaria, A. Fachechi and G. Macorini, “On the cusp anomalous dimension in the ladder limit of N = 4 SYM”, JHEP 160...

    2016 arXiv

  57. [65]

    Quantum spectral curve and structure constants in N = 4 SYM: cusps in the ladder limit

    A. Cavagli` a, N. Gromov and F. Levkovich-Maslyuk,“Quantum spectral curve and structure constants in N = 4 SYM: cusps in the ladder limit” , JHEP 1810, 060 (2018), 1802.04237

    2018 arXiv

  58. [66]

    Dyson equations for correlators of Wilson loops

    D. Correa, P. Pisani, A. Rios Fukelman and K. Zarembo, “Dyson equations for correlators of Wilson loops” , JHEP 1812, 100 (2018), 1811.03552

    2018 arXiv

  59. [67]

    Scalar insertions in cusped Wilson loops in the ladders limit of planar N = 4 SYM

    J. McGovern, “Scalar insertions in cusped Wilson loops in the ladders limit of planar N = 4 SYM” , JHEP 2005, 062 (2020), 1912.00499

    2020 arXiv

  60. [68]

    On the Dyson-schwinger Equations Approach to the Large N Limit: Model Systems and String Representation of Yang-Mills Theory

    S. R. Wadia, “On the Dyson-schwinger Equations Approach to the Large N Limit: Model Systems and String Representation of Yang-Mills Theory” , Phys. Rev. D 24, 970 (1981)

    1981

  61. [69]

    Loop Equations and 1/N Expansion

    A. A. Migdal, “Loop Equations and 1/N Expansion” , Phys. Rept. 102, 199 (1983)

    1983

  62. [70]

    Planar RG flows on line defects

    I. Nagar, A. Sever and D.-l. Zhong, “Planar RG flows on line defects” , JHEP 2406, 110 (2024), 2404.07290

    2024 arXiv

  63. [71]

    The 1/2 BPS ’t Hooft loops in N=4 SYM as instantons in 2d Yang-Mills

    S. Giombi and V. Pestun, “The 1/2 BPS ’t Hooft loops in N=4 SYM as instantons in 2d Yang-Mills” , J. Phys. A46, 095402 (2013), 0909.4272

    2013 arXiv

  64. [72]

    A novel long range spin chain and planar N = 4 super Yang- Mills

    N. Beisert, V. Dippel and M. Staudacher, “A novel long range spin chain and planar N = 4 super Yang- Mills” , JHEP 0407, 075 (2004), hep-th/0405001. • N. Beisert, “The su(2∣2) dynamic S-matrix” , Adv. Theor. Math. Phys. 12, 945 (2008), hep-th/0511082

    2004 arXiv

  65. [73]

    Massive N=2 Gauge Theories at Large N

    J. Russo and K. Zarembo, “Massive N=2 Gauge Theories at Large N” , JHEP 1311, 130 (2013), 1309.1004

    2013 arXiv

  66. [74]

    Wilson loops in large N field theories

    J. M. Maldacena, “Wilson loops in large N field theories” , Phys. Rev. Lett. 80, 4859 (1998), hep-th/9803002

    1998 arXiv

  67. [75]

    Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics

    S. S. Pufu, “Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics”, Phys. Rev. D 89, 065016 (2014), 1303.6125

    2014 arXiv

  68. [76]

    Topological disorder operators in three-dimensional conformal field theory

    V. Borokhov, A. Kapustin and X.-k. Wu, “Topological disorder operators in three-dimensional conformal field theory” , JHEP 0211, 049 (2002), hep-th/0206054. • V. Borokhov, A. Kapustin and X.-k. Wu, “Monopole operators and mirror symmetry in three-dimensions” , JHEP 0212, 044 (...

    2002 arXiv

  69. [77]

    Table of integrals, series, and products

    I. Gradshteyn and I. Ryzhik, “Table of integrals, series, and products” , Elsevier Science (2014). 59

    2014

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