All-genus calculation of Wilson loops using D-branes

Bartomeu Fiol; Nadav Drukker

REVIEW

All-genus calculation of Wilson loops using D-branes

Nadav Drukker, Bartomeu Fiol

High Energy Physics - Theory · Submitted 14 Jan 2005 · 31 references

Pith's verdict: The circular-loop D3-brane and its all-genus reading are the real contribution, and the matrix-model match is an independent check rather than a fit; the C4 choice is the one soft spot, and the authors flag it themselves.

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CitationBartomeu Fiol, Nadav Drukker. "All-genus calculation of Wilson loops using D-branes." arXiv:hep-th/0501109 (2005). https://pith.science/paper/TXD3GZXV

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Editor's note

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Short version: the circular-loop D3-brane is the result worth your time, and it holds up. The straight-line case is Rey-Yee's and they say so in Section 2, so the new content is the circle: the solution sin η = κ⁻¹ sinh ρ, the induced AdS₂×S² geometry with radii L√(1+κ²) and Lκ, and the reading of the brane action as the sum over all genera at leading α′. The action (3.16) expands to −k√λ − k³λ^{3/2}/(96N²) + …, and the Drukker-Gross matrix model ODE (3.24) collapses at large N to (3.26), whose solution is exactly (3.16). That is a real cross-check: a perturbative rainbow resummation on one side, a DBI computation on the other. Nothing in the derivation is hidden; a competent group could redo it from the text. The boundary Legendre transforms in 3.2 are the part I'd want a student to work through, since the bulk alone gives only the k³ term and the linear piece comes entirely from the boundary terms — that is a nice, checkable structural point, not a hand-wave. The soft spot is the one the stress-test names, and it lands. Section 3.5 is the honest tell: the conformally related C′₄ = C₄ + dΛ₃ gives a vanishing bulk action, i.e. the straight-line answer, so the finite circular result is selected by the choice of representative, not forced by the bulk equations. The authors say as much — the Wess-Zumino boundary term is left open in 2.2, and they call for a better understanding of it. What keeps this from being serious is that the matrix-model match is independent of the C₄ choice, so the concern is 'we'd like a principle (κ-symmetry would do it)' rather than 'the number might be wrong.' Two smaller things: supersymmetry is verified only for the line (2.3); the circle claim in 3.1 is asserted, and the projector algebra would be worth displaying. And the 't Hooft section the authors themselves describe as flawed — read it as exploratory, not as a result. One correction to the record: the classifier found no stated limitations, which is wrong; the paper is unusually candid about its gaps. Who should read it: anyone using D-branes for Wilson loops, anyone working on finite-N corrections to strong-coupling observables, and anyone thinking about the k³/N² scaling that shows up here and in Douglas-Shenker. The k-string comparison in the Discussion is suggestive, not established. Send it to referees.

Referee report

Significance

If correct, this is a genuinely useful new prescription: it resums, at leading order in α', the entire genus expansion of multiply-wrapped Wilson loops into a single classical DBI+WZ action, which is exactly the kind of non-planar information that had not previously been accessible. The cross-check against the matrix model is a real independent validation rather than a fit: the exact finite-N ODE (3.24) reduces at leading large N to (3.26), whose solution is precisely (3.16). The paper also makes falsifiable predictions for the k³λ^{3/2}/96N² and k⁵λ^{5/2}/10240N⁴ coefficients, and the arithmetic in (3.17) is internally consistent. The extension to 't Hooft loops and the S-duality discussion add scope. The work is well organized and the derivations are presented step by step.

Major objections (1)

[Sections 2.2, 3.2, 3.5; Eqs. (2.2), (3.31)] The finite circular action (3.16) is not determined by the bulk equations of motion alone: it depends on which representative C4 of the Ramond-Ramond four-form potential is used in the Wess-Zumino term. Section 3.5 makes this explicit, showing that the conformally related potential C'4 = C4 + dΛ3 in (3.31) yields a vanishing bulk action (the straight-line answer), whereas the authors' C4 in (2.2) yields the non-trivial (3.16). The authors select (2.2) on grounds of symmetry and absence of singularities along the loop, and they explicitly leave the gauge-invariant completion of the Wess-Zumino boundary term open (Section 2.2: 'It would be good to get a better understanding of this issue'). This is a load-bearing choice for the central result, and it is currently fixed by naturalness plus an a posteriori matrix-model match. A concrete test that would remove the ambiguity: establish κ-symmetry of the circular solution. Section 3.1 asserts that the circle 'also preserves half the supersymmetries' but does not display the projector algebra that Section 2.3 carries out for the line. If the circle solution is shown to be κ-symmetric, the Wess-Zumino boundary term should be fixed by the requirement that the configuration be supersymmetric, which would convert the naturalness choice into a derived one. I regard this as a correctness-risk concern rather than an error, because the matrix-model agreement is an independent check; but the paper would be substantially strengthened by either supplying the κ-symmetry argument or stating more sharply that the C4 choice is validated only a posteriori.

Minor objections (6)

[Section 3.1] The statement that the circular solution preserves half the supersymmetries is asserted without the projector computation given for the straight line in Section 2.3. Either display the analogous algebra or argue explicitly that the circle solution inherits the supersymmetries of the line through the conformal transformation of Section 3.5, noting that the conformal transformation also changes C4 by dΛ3 and explaining why the inherited supersymmetry selects the representative used.
[Section 4.2; Ref. [26]] The perturbative 't Hooft-loop calculation in Section 4.2 is stated to be 'Based in part on a collaboration between N.D. and N. Itzhaki [26]', and Ref. [26] is listed as unpublished. Since this section supplies the only direct gauge-theory comparison for the 't Hooft loop, the reader should be told which parts rest on unpublished work and which are self-contained here.
[Section 4.2; Eqs. (4.5), (4.13)] The two expressions for the 't Hooft-loop expectation value disagree in powers of π and in the overall power of N, and the authors acknowledge this. It would help to state explicitly which discrepancy is expected to be absorbed by the determinant of massive fluctuations and which by the normalization of the 't Hooft operator, so that a future calculation has a clear target.
[Section 4.1] The symbol κ is reused with a different definition in the magnetic case (κ = πk/√λ̃) than in the electric case (κ = k√λ/(4N)). Since the two sections are read together and the validity conditions are compared at the end of Section 3.3, a short explicit reminder at the point of redefinition would prevent confusion.
[Section 5] The identification of a single D3-brane with a single-trace Wilson-loop operator, and of multiple branes with multiple traces, is presented as a guess ('It's natural to guess'). This is appropriately hedged, but it would be worth flagging explicitly as a conjecture to be tested rather than a result of the paper.
[Throughout] There are several typographical errors that should be corrected: 'lo lie' in Section 2.1, 'fasion' in Section 4.1, 'sereval' and 'trance' in Section 5, and 'precicely' in Section 4.2. Equation (3.18) and the surrounding heuristic argument for the λ^{(6p-3)/4}/N^{2p} scaling are clear, but the absence of a heuristic for the k³ scaling is noted by the authors and could be stated once more plainly as an open question.

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The paper

The paper claims

A single D3-brane carrying electric flux, ending on a Wilson-loop contour at the boundary of AdS, reproduces the loop's expectation value including all higher-genus string corrections at leading order in the coupling.

The reading

In the standard holographic recipe a Wilson loop is computed from a fundamental string world-sheet hanging from the loop into anti-de Sitter space. That picture degrades when the loop is multiply wound $k$ times, because one then has $k$ coincident strings that can interact, and their interactions are exactly the string-loop (higher-genus) corrections nobody had summed. The paper's claim is that the right object in that regime is not many strings but one D3-brane with electric flux on its world-volume, whose induced geometry is $AdS_2$ times a two-sphere. Solving the Dirac-Born-Infeld plus Wess-Zumino action for the straight line and the circle, and adding the boundary terms that swap the transverse coordinate and the gauge field for their conjugate momenta, gives a closed expression for the circular loop. Expanded in $1/N$, that expression reproduces the leading $k$ times the square root of the 't Hooft coupling and then a whole tower of $1/N^2$ corrections whose coefficients match the zero-dimensional Gaussian matrix model obtained by summing rainbow and ladder diagrams. If correct, a classical brane calculation has quietly done the work of summing over all genera of string surfaces.

What carries the argument

The carrier is a D3-brane embedded in $AdS_5$ whose world-volume metric is $AdS_2 × S^2$, with the $AdS_2$ curvature radius $L√(1+κ^2)$ and the sphere radius $Lκ$, and with a constant conjugate momentum $Π=k$ for the world-volume electric field, $k$ being the number of coincident strings or the winding of the loop. The straight-line case uses the ansatz $y=r/κ$; the circular case uses adapted coordinates in which the solution is $sin η = κ^{-1} sinh ρ$, so that near the boundary it reduces to the straight-line spike, as any smooth loop must in the ultraviolet. Two ingredients do the real work: the Legendre transform of the radial coordinate, which replaces the coordinate with its normal momentum and makes the action a functional of the correct variable, and the Legendre transform of the gauge field, which replaces $A$ with $Π=k$ via a total derivative. Each term of the action is linearly divergent, and the divergences cancel only in the sum.

Extended reading notes

Core claim

The paper constructs D3-brane solutions in $AdS_5$ that pinch off at the boundary of AdS along the Wilson-loop contour, and shows that their on-shell action reproduces the field-theory answer. For the infinite straight line the bulk Dirac-Born-Infeld term is exactly cancelled by the Wess-Zumino term, and the two Legendre-transform boundary terms cancel each other, leaving $S=0$, i.e. $W=1$, as supersymmetry requires; the same solution is shown to preserve the same half of the supersymmetries as the string solution. For the circular loop the bulk combination is finite, and after the boundary terms one obtains $S=-2N[κ√(1+κ^2)+sinh^{-1}κ]$ with $κ=k√λ/(4N)$, where $k$ is the winding number. Expanding in small $κ$ gives $-k√λ - k^3λ^{3/2}/(96N^2) + k^5λ^{5/2}/(10240N^4)+…$, so the leading term is the $k$-times-string answer and the rest are $1/N^2$ corrections. The authors then show that the finite-$N$ Gaussian matrix model of the circular loop obeys a differential equation which, at large $N$, reduces to $dF/dκ = -4√(1+κ^2)$, whose integral is precisely the brane action. The same construction with a magnetic field on the two-sphere, reached by S-duality, gives the 't Hooft loop with the identical functional form, and is compared to a weak-coupling magnetic-monopole calculation including the zero-mode determinant.

Load-bearing premise

The finite circular-loop answer depends on a choice of boundary terms and of the four-form potential, and the authors state that they did not find a compelling gauge-invariant completion of the Wess-Zumino boundary term, nor do they resolve why a conformally related potential would give a vanishing bulk action.

Editorial extensions

If this is right

The $k^3λ^{3/2}/(96N^2)$ term in the circular Wilson loop is identified as the first string-loop correction, giving a concrete target for any direct genus-one world-sheet computation in $AdS_5×S^5$.
The full D3-brane action supplies all orders in $1/N$ that survive at large $λ$, so the $1/N$ expansion of the circular loop is determined without resumming Feynman diagrams.
The 't Hooft loop, obtained by the same ansatz with magnetic flux, has the same functional form as the Wilson loop under S-duality, and its weak-coupling expansion matches a semiclassical monopole calculation up to a discrepancy in powers of $N$ and $π$.
The $k^3/N^2$ scaling of the leading correction parallels the $k^3/N^2$ term in the Douglas-Shenker formula for $k$-string tensions in confining theories, suggesting a common origin in the interaction among coincident strings.
The prescription is expected to extend to any smooth contour, since all divergences are ultraviolet and the brane asymptotically approaches $AdS_2 × S^2$; the antiparallel-line pair is named as the next case to compute.

Reading between the lines

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

If one D3-brane corresponds to one trace in the Wilson-loop operator, then a multi-trace loop should be described by several branes, which would make this system a natural place to look for a non-Abelian Born-Infeld action rather than merely assuming one.
The match requires only $λ≫1$ and $Nκ≫1$, not the strong-coupling regime where the brane is weakly curved, so the agreement extends to $k=1$; that is a stronger statement than the geometric validity argument in the text would suggest, and it hints that the brane description is capturing something protected rather than merely a saddle point.
The same Legendre-transform bookkeeping should apply to D-branes of other dimensions ending on other defects, so the method is plausibly a general recipe for resumming handle-counting on any holographic defect, not a trick specific to Wilson loops.
Because the result is a classical brane action, it says nothing about D-instanton corrections; the authors note those should match instanton contributions that the Gaussian matrix model does not capture, which would be a clean independent check of the whole picture.

Original abstract

The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS. For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves. In such cases a better description of the system is in terms of a D3-brane carrying electric flux. We find such solutions for the single straight line and the circular loop. The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'. The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,770 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS. For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves. In such cases a better description of the system is in terms of a D3-brane carrying electric flux. We find such solutions for the single straight line and the circular loop. The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'. The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS.	background 1.00	0.03	0.03	asserted 1.00
s1	For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves.	background 0.96	0.08	0.02	hedged possibility 0.99
s2	In such cases a better description of the system is in terms of a D3-brane carrying electric flux.	method 0.65	0.13	0.12	asserted 0.87
s3	We find such solutions for the single straight line and the circular loop.	contribution 0.61	0.95	0.08	asserted 1.00
s4	The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'.	result 0.97	0.90	0.50	asserted 1.00
s5	The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.	result 0.91	0.70	0.25	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
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references and citing sentences
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levels run

P abstract

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C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** A depiction of the D3-brane solution describing th

Figures reproduced from arXiv:hep-th/0501109 by the authors.

References

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Near-threshold flux tube excitations in large N gauge theory have a density of states that matches between a ladder diagram model and folded strings in AdS, and large-distance Wilson loop correlators share the same po...
Ortho-symplectic interface line operators in $\mathcal{N}=4$ SYM theories
hep-th 2026-10 conditional novelty 6.0 of 10

For half-BPS interfaces in ortho-symplectic N=4 SYM, Wilson and vortex line operators obey proposed S-dualities proved analytically for Abelian so(2) interfaces and matched in q-series for general ranks.
Giant Wilson loops from Fredholm determinants
hep-th 2026-10 accept novelty 6.0 of 10

A Fredholm determinant and Tracy-Widom/WKB method gives the leading and first subleading 1/N contributions to symmetric and antisymmetric giant Wilson loop free energies, reproducing earlier matrix-model results and t...
Continuous symmetries and charge measurement of boundary operators in holography
hep-th 2026-02 conditional novelty 6.0 of 10

Continuous symmetry operators in holography are U-shaped hanging brane bound states (D5-KK in Type IIB, M5-KK in M-theory) whose worldvolume couplings reproduce the Gauss-law symmetry operators and measure charges of ...
Oscillons in AdS space
hep-th 2024-12 conditional novelty 6.0 of 10

Simulations show long-lived oscillons in anti-de Sitter space, with recurrence of decayed waves and a transition to a persistent oscillatory state as the AdS radius shrinks.
Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
hep-th 2019-08 conditional novelty 6.0 of 10

The paper expresses connected correlators of multiply-wound Wilson loops in N=4 SYM through explicit matrix-trace formulas, including a new inverse relation verified numerically up to order eight.
More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
hep-th 2018-11 accept novelty 6.0 of 10

Bulk-defect correlators on the 1/2-BPS Wilson loop in N=4 SYM are computed exactly at planar order and expressed as contour integrals over Quantum Spectral Curve Q-functions, matching both weak-coupling perturbation t...
Half-BPS Wilson loop and AdS$_2$/CFT$_1$
hep-th 2017-06 accept novelty 6.0 of 10

Tree-level AdS2 Witten diagrams give the strong-coupling four-point functions of protected operator insertions on the 1/2-BPS Wilson line, yielding anomalous dimensions of two-particle operators and matching a localiz...
Wilson Loops in 5d N=1 SCFTs and AdS/CFT
hep-th 2012-12 accept novelty 6.0 of 10

Wilson loop expectation values in five-dimensional N=1 superconformal theories, computed by localization and by probe strings and D4-branes in the dual massive IIA background, agree at leading large N for fundamental,...
Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
hep-th 2012-02 conditional novelty 6.0 of 10

A D3-brane probe computation of the Lagrangian density one-point function around a static quark matches two prior results, motivating an exact all-N, all-coupling formula in terms of Laguerre polynomials.
Line Operator Index on S1 $\times$ S3
hep-th 2012-01 conditional novelty 6.0 of 10

A general, monopole-bubbling-corrected index formula for BPS line operators on S1 x S3 is derived and checked against S-duality and holographic string/D5-brane spectra.
The Spectrum of Excitations of Holographic Wilson Loops
hep-th 2011-01 conditional novelty 6.0 of 10

The excitation spectrum of the D3 brane dual to a half-BPS Wilson loop organizes into short multiplets of OSp(4*|4), with the fundamental string modes forming the ultra-short multiplet.
Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
hep-th 2009-06 conditional novelty 6.0 of 10

Correlators of 1/8 BPS Wilson loops with chiral-primary local operators on a two-sphere are captured by a two-matrix model derived from two-dimensional Yang-Mills, and its planar strong-coupling limit matches the AdS5...
Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
hep-th 2008-09 conditional novelty 6.0 of 10

The authors construct 1/6-BPS Wilson loops in ABJM theory, compute their planar vacuum expectation value to order lambda squared as (5/3) pi^2 lambda^2, and find a dual fundamental string ending on a circle.
Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals
hep-th 2008-09 conditional novelty 6.0 of 10

Supersymmetric Wilson loops in the N=6 Chern-Simons theory preserve 1/6 of the supercharges, are computed to two loops at weak coupling, and are matched to smeared fundamental strings, D2-branes and D6-branes in AdS4 x CP3.
Probing N=4 SYM With Surface Operators
hep-th 2008-05 accept novelty 6.0 of 10

Three independent calculations (weak-coupling gauge theory, probe D3-branes, and bubbling supergravity) give matching answers for surface-operator observables in N=4 super Yang-Mills.
Supersymmetric Wilson loops on S^3
hep-th 2007-11 conditional novelty 6.0 of 10

A new almost complex structure on AdS4 x S2 makes the string duals of a family of supersymmetric Wilson loops on S3 pseudo-holomorphic, and loops on S2 appear to reduce to two-dimensional Yang-Mills.
Comments on operators with large spin
hep-th 2007-08 accept novelty 6.0 of 10

The cusp anomalous dimension of N=4 super Yang-Mills equals the energy density of a flux configuration on AdS3 x S1, and in a large-spin, large-charge limit the string reduces to a solvable O(6) sigma model.
1/2-BPS states in M theory and defects in the dual CFTs
hep-th 2007-04 conditional novelty 6.0 of 10

Supersymmetric brane geometries in AdS7 x S4 and AdS4 x S7 are shown to be completely specified by one harmonic function of two variables, with a classification of boundary conditions that yield smooth eleven-dimensio...
Bubbling Defect CFT's
hep-th 2006-04 conditional novelty 6.0 of 10

A BPS equation system for the gravitational duals of half-BPS domain wall operators in N=4 SYM is derived and reduced to a single second-order PDE, without constructing explicit solutions.
Multiply wound Polyakov loops at strong coupling
hep-th 2006-03 conditional novelty 6.0 of 10

Multiply wound Polyakov-Maldacena loops in strongly coupled N=4 super Yang-Mills receive D5-brane corrections of order k^{5/3}/N^{2/3}, hinting at a Gross-Witten-like transition.
Roadmap on Wilson loops in 3d Chern-Simons-matter theories
hep-th 2019-10 accept novelty 5.0 of 10

The review organizes the state of the art on ABJ(M) Wilson loops and introduces a manifestly reparametrization-invariant superconnection formulation of the 1/6 BPS fermionic loop.
Wilson Loops as D3-Branes
hep-th 2006-12 accept novelty 5.0 of 10

Integrating out W-bosons in a Coulomb-branch configuration shows that a D3-brane with k strings inserts a half-BPS Wilson loop in the k-th symmetric representation, and more generally in any chosen representation of U(N).
Universality of k-string Tensions from Holography and the Lattice
hep-th 2006-04 conditional novelty 5.0 of 10

Wilson loop expectation values in SU(N) gauge theory take the form dim R exp(-sigma_k A), with the string tension depending only on the N-ality k, not on the specific representation.
Bubbling Geometries for Half BPS Wilson lines
hep-th 2006-01 conditional novelty 5.0 of 10

Half-BPS Wilson line operators in N=4 SYM correspond, via necessary IIB supersymmetry conditions, to supergravity backgrounds whose boundary black-and-white pattern matches the eigenvalue distribution of the Gaussian ...
The AdS/CFT Correspondence
gr-qc 2014-12 accept novelty 2.0 of 10

A self-contained review of the AdS/CFT correspondence: its string theory origin, its dictionary of bulk-to-boundary mappings, and its applications to black holes, fluids, and quantum gravity.

How later papers used it

103 later papers cite it

Evidence: substantial. 97 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 24 of the 235 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 3 used its method or tool.

Uses its method or tool 3 of 7 papers with this label

Followed this paper in adding the boundary contribution to the action, finding that the action vanishes and the dual line operator's vacuum expectation value equals one.

Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3 (2008) · 0.80 · paraphrased: the licence does not allow quoting
Followed this paper's approach using the differential equation satisfied by Z(τ).

Eigenvalue instantons in the spectral form factor of random matrix model (2018) · 1.00 · paraphrased: the licence does not allow quoting
Picked a gauge that reproduces the correct circular Wilson loop expectation value, namely that used in this paper.

Holographic Entanglement Entropy of the Coulomb Branch (2020) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

102 arXiv papers cite this in 226 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 162 sentences without a confident label

Builds on it 1 paper

This was done for purely electric states in [ref] , who found a probe D3 brane embedded in $AdS_5$ giving the D3 description of an straight open Wilson line for an electrically charged $1/2$ BPS state; one can readily extend that description to other $1/2$ BPS states in the same $SL(2,)$ orbit (see also [ref] for a general realization of $1/2$ BPS Wilson lines in arbitrary representations, in terms of D5 or D3 branes).

Dyonic D3 branes · Introduction · 0.90

Uses its method or tool 7 papers

Now, the standard prescription to renormalize the action is to perform Legendre transforms on some of the worldvolume fields [ref] .

On the D5-brane description of $\frac{1}{4}$-BPS Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory · String charge and on-shell action · 0.82
The flux quantization condition [ref] implies [equation] We use the gauge symmetry [ref] and set [equation] Actually, the final result is independent of this gauge choice as far as we use the Legendre transformation prescription for the 2-form gauge field as in [ref] .

M5-branes and Wilson Surfaces in AdS$_{7}$/CFT$_{6}$ Correspondence · M5-brane wrapping $_3 ×S^3$ · 0.84
Finally we determine the value of the action ([ref]) for the ansatz ([ref]) and we find [equation] However this is not full story since we should perform a Legendre transformation in this action in order to write it as a functional of $Π$ instead of $f$ [ref] .

Wilson Loops from D-branes in AdS(4) X CP**3 with B-NS Holonomy · Description of Wilson loops in Supergravity Dual $AdS_4×CP^3$ with $B_NS$ Holonomy · 0.95

Compares with it 6 papers

The result supports that [equation] Thus [ref] reduces to [equation] This is nothing but the result of [ref] .

A tunneling picture of dual giant Wilson loop · Consistency with $J→0$ limit · 0.94
This agrees with the localization prediction [ref] , which can be obtained by evaluating ([ref]) at strong coupling with $k/N$ fixed (note that, as already discussed above, the result in ([ref]) applies to the more general 1/8-BPS Wilson loops, which are just related to the 1/2-BPS one by a rescaling of the coupling $λ→λ(1-a^2)$).

Giant Wilson Loops and AdS$_2$/dCFT$_1$ · D3-brane solution in $AdS_5×S^5$ · 0.93
This is not merely analogous to what we are arguing for: a precise match between the winding number $k$ and our inverse temperature $β$ can be made and, as we show in <ref>, our single-eigenvalue instantons exactly match the D-brane results of [ref] .

Entropy and Spectrum of Near-Extremal Black Holes: semiclassical brane solutions to non-perturbative problems · Lessons for Gravity · 0.95

Cites it as support 2 papers

In fact, as was shown in [ref]

D-brane Description of New Open String Solutions in AdS(5) · D5-brane on $S^4$ and D3-brane on $S^2$ · 0.97
The circular loop and the straight line also preserve a part of the supersymmetry of SYM, namely they are BPS objects, and therefore corresponding D3-brane solutions should preserve some of global supersymmetry of type IIB supergravity and, as also shown in [ref] , so do they.

Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence · BPS conditions and the uniqueness of the solution · 0.96

Cites it as background 35 papers

Let us give a brief review of the D3-brane solution derived in [ref] , which will be useful for later discussions.

Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence · A review of the Drukker-Fiol D3-brane solution · 0.92
It was first introduced in [ref] .

The Spectrum of Excitations of Holographic Wilson Loops · Review of the classical configurations · 0.95
More precisely the Wilson loop in the large-rank symmetric representation is dual to the D3-brane on the $AdS_2×S^2$ subspace inside $AdS_5$ [ref] while the one in the antisymmetric representation is dual to the D5-brane on $AdS_2 ×S^4$, where $S^4$ is a subspace inside $S^5$ [ref] .

Giant Wilson Loops and AdS$_2$/dCFT$_1$ · Giant Wilson loops and holographic dual · 0.82

Discussion

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