On the highest transcendentality in N=4 SUSY

A.V. Kotikov; L.N. Lipatov

REVIEW

On the highest transcendentality in N=4 SUSY

A.V. Kotikov, L.N. Lipatov

High Energy Physics - Theory · Submitted 20 Nov 2006 · 32 references

Pith's verdict: The perturbative core — explicit kernel plus the integer-coefficient proof — is solid and worth using; the strong-coupling headline is leading-order only and the abstract states it more strongly than the derivation supports.

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arXiv IDhep-th/0611204 (version 2)

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CitationA.V. Kotikov, L.N. Lipatov. "On the highest transcendentality in N=4 SUSY." arXiv:hep-th/0611204 (2006). https://pith.science/paper/5JV2ACCU

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Two things worth knowing up front. The perturbative half is real work and holds up. The strong-coupling headline is softer than the abstract makes it sound, and the authors know it — they say so in the text and then don't say it in the abstract. That gap is the main thing to flag to a reader who only skims abstracts, which is most of us. Sections 3 and 4 are the meat. Reducing the ES equation to a_{n,eps} = sum K_{n,n'}(delta - a) with the kernel in closed form (Eqs. 40-41, plus the Mellin-Barnes version) is a genuine step, and the integer-coefficient proof in Section 4 is a real combinatorial argument — the three-factor split of T_{n,n';R} in Eq. 62 is the whole trick and it works. Radius of convergence, the essential singularity at eps = 0, the analytic structure in j: all fine, all checkable. That part deserves to be used. The strong-coupling part is where I'd slow down. The authors are upfront — Section 6 says 'there is an uncertainty in the limiting form of the ES equation,' Section 9 says 'assuming that this singular behavior is valid also for large z,' and Appendix D parks the corrections as future work. So the stress-test concern lands: abstract:s8 says the BES singular solution 'reproduces' the string prediction, but Eq. 173 gives 2 sqrt(2) g - 1/2 - ..., while Eq. 175 gives 2 sqrt(2) g - 0.662. That is leading order only, and the NLO coefficient is roughly a quarter off. The Y_n branch of the recurrence is also discarded on a plausibility argument, not a proof. And since the BES phase was built to restore string agreement, the leading 2 sqrt(2) g is partly by construction — though extracting it from the singular solution is still not nothing. One more: several key results are credited to ref. [24], Lipatov's unpublished Potsdam talk. Fine as provenance, but it means a reader cannot check the earlier version. The ES oscillation result (Eq. 130) is arguably the more interesting finding — ES fails to match string, BES stabilizes — and the paper states that plainly. Who should read it: anyone working the ES/BES equations analytically. Cite the perturbative machinery; cite the strong-coupling asymptotics with the caveats attached. Send it out — the perturbative core will survive refereeing and the strong-coupling section will get the scrutiny it needs.

Referee report

Significance

The perturbative part is a genuine and durable contribution: the closed-form kernel, its Mellin–Barnes representation, and the reduction to a linear algebraic system give an analytic handle on the all-orders large-spin anomalous dimension that complements the numerical and KLV approaches. The integer-coefficient argument, if completed, would establish the Eden–Staudacher transcendentality hypothesis as a theorem rather than a conjecture, and the functional relations of Section 5 are a useful structural result valid at all coupling. The strong-coupling analysis is more tentative and its headline claim is weaker than the abstract suggests; the value of that part lies mainly in the observation that the BES singular solution lands on the leading string prediction, which is a consistency check rather than an independent derivation.

Major objections (4)

[Abstract (s8); Section 8, Eqs. (173), (175); Section 9] The abstract states without qualification that the BES singular solution 'reproduces the anomalous dimension predicted from the string side' (abstract:s8), but the text establishes agreement only at leading order. Eq. (173) gives 2√2 g − 1/2 − √2/(32g), while the string prediction quoted in Eq. (175) is 2√2 g − (3π/2)ln 2 ≈ 2√2 g − 0.662, so the next-to-leading coefficients differ by roughly 24%. The authors are candid about this in Section 9 and in Appendix D, where the missing corrections are attributed to terms not kept in the singular solution, but the abstract does not carry that qualification. Since the abstract's final sentence is the paper's most visible claim, it should be reworded to say that the leading 2√2 g term is reproduced and that the NLO coefficient is obtained only approximately.
[Section 6, Eqs. (109), (112), (127), (130); Section 8, Eq. (166)] The strong-coupling limit is not unique as presented. Eq. (109) and Eq. (127) differ by the replacement of ~z' with z' on the unit contour, and they lead to different kernels (Eq. (112) versus the kernel implicit in Eq. (127)); the authors acknowledge 'there is an uncertainty in the limiting form of the ES equation' and repeat the caveat for BES in Section 8. Because the oscillating ES result of Eq. (130) and the BES result of Eq. (173) both follow from the choice ~z' → z', the reader cannot tell whether the oscillation is a property of the ES equation or an artifact of the limiting procedure. A concrete and feasible test is available: Refs. [12] and [25] report numerical solutions of the BES equation at intermediate coupling, and a comparison of Eq. (173) with those numbers at, say, g = 2–5 would either support the singular solution or expose where it departs. The paper cites both references but performs no such comparison, and adding one would materially strengthen the strong-coupling section.
[Section 4, Eqs. (52), (62), (63)] The integer-coefficient claim (abstract:s2) is the paper's headline 'proof', but the argument following Eq. (63) is a sketch that treats only the case where 2R+n+n' contains a single prime factor p. The text argues that the two binomial factors supply the needed factor of p and that when p divides both n and n' the third factor 2n/(2R+n+n') restores it, but it does not address prime powers p^a with a > 1, which is precisely where a p-adic valuation argument is required. Since the conclusion that all T_{n,n';R} are integers is load-bearing for the integer coefficients of the ζ-products, the valuation argument should be completed in full, or a table of T_{n,n';R} for small n, n', R should be supplied so that the claim can be checked directly.
[Abstract (s3); Section 3, Eqs. (40)–(41); Section 4, Eq. (46)] The abstract states that 'the radius of convergency of the perturbation theory is found' (abstract:s3), but what Sections 3 and 4 actually establish is the radius of convergence of the series for the kernel K_{n,n'}(ε), namely the singularity at ε² = −4. The radius of convergence of the anomalous-dimension series itself is governed by the spectrum of the operator K̂(ε), which is not determined; Section 4 only notes that K_{1,1}(ε) ≈ 8/(3ε) as ε → 0 and that iteration in K̂ therefore works only for sufficiently large ε. The abstract and the corresponding sentence in Section 3 should be reworded to make clear which series' radius is being reported.

Minor objections (7)

[Appendix A, Eq. (A2)] In the definition of the magnon charges q_r(x^±) both terms in parentheses are written as 1/(x^+)^{r−1}; the second should presumably be 1/(x^−)^{r−1}.
[Section 5, Eq. (86)] The vanishing of the contour integral in Eq. (86) is attributed to 'the symmetry of χ(z') under the substitution z' → −1/z'', but χ on the second sheet is not equal to χ on the first, and the measure (z'²+1)/z'² is not invariant under z' → −1/z'. A sentence spelling out why the integral vanishes would help the reader follow the anti-symmetrization that leads to Eq. (88).
[Section 3, Eq. (19)] The ansatz (19) is introduced as 'we search the solution ... in the form [24]' without an argument that it is the general solution. The completeness is effectively established later, in Section 5, where Eq. (92) identifies the coefficients with the Laurent expansion of an analytic function at infinity; a forward reference at Eq. (19) would make the logic clearer.
[Section 6, Eq. (65)] The expression for γ near ε² = −4 is obtained after assuming that the regular part of K_{n,n'} at ε² = −4 'does not depend essentially on n and n''. The formula is presented without flagging that it is an approximation; a phrase in the text would prevent it being read as exact.
[Section 4 title and throughout] The same object is called the 'SE equation' in the title of Section 4 and the 'ES equation' elsewhere; the notation should be made uniform.
[Section 8 and References] Several typographical errors should be corrected: 'Frolov-Zeitlin' in Section 8 should read 'Frolov-Tseytlin'; 'maid by us' in Section 9 should read 'made by us'; 'week coupling' in Appendix A should read 'weak coupling'; 'convergency' in the abstract and Section 3 should read 'convergence'; 'Kroneker' in Section 3 should read 'Kronecker'; and in the reference list 'Gurci' should read 'Curci' and 'Kosover' should read 'Kosower'.
[Reference [24]] Several structural inputs — the ansatz (19), the kernel (40), and the functional relation (88) — are attributed to the Potsdam talk [24], which is unpublished. The text does reproduce the derivations, so this is not a blocking issue, but the reliance on an unpublished source for the origin of the ansatz is worth a note.

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The paper

The paper claims

The large-spin anomalous dimension in N=4 super-Yang-Mills is shown to be an integer-coefficient sum of products of zeta values, and the integral equation that governs it is reduced to a solvable linear system.

The reading

In N=4 supersymmetric Yang-Mills theory the anomalous dimension of twist-2 operators grows like $4g^2$ times a function of the coupling at large spin, and Eden and Staudacher had written down an integral equation that fixes that function at every order of perturbation theory. This paper turns that integral equation into an infinite set of linear algebraic equations for coefficients $a_{n}$, with the kernel $K_{n,n'}$ computed in closed form as a Mellin-Barnes integral and as a sum of hypergeometric functions. With the kernel in hand the authors prove the Eden-Staudacher conjecture: every perturbative coefficient of the anomalous dimension is a sum of products of Euler zeta values of maximal transcendentality, weighted by integer numbers, because the combinatorial factor in the kernel is itself an integer. They also locate the radius of convergence of the weak-coupling series and show that at $g=0$ (infinite coupling) the kernel develops an essential singularity. The same machinery is then applied to the Beisert-Eden-Staudacher equation, which adds the crossing-symmetry phase, and its singular solution at strong coupling reproduces the leading $2^{3/2}g$ behaviour predicted from the string side of the AdS/CFT correspondence.

What carries the argument

The load-bearing object is the kernel $K_{n,n'}(g)$ of the linear system, expressed as a Mellin-Barnes integral with a zeta function and a ratio of Gamma functions, or equivalently as a sum of ${}_4F_3$ hypergeometric functions. It is what makes the integral equation tractable: it converts an equation for a function into an infinite matrix equation, and its explicit form lets the authors read off the transcendentality and integrality properties of the perturbative coefficients. A second piece of machinery is the conformal map $z = j + (j^2+1)^{1/2}$ from the Laplace variable $j$ to a variable $z$ in which the equation becomes the functional relation $1/2(chi(z) + chi(-1/z)) = 1$, relating the solution on the two sheets of the Riemann surface. In the strong-coupling limit this relation degenerates and the singular solution is built from Bessel functions $I_n(2/g)$.

Extended reading notes

Core claim

The paper's central claim is that the Eden-Staudacher equation can be rewritten as the linear system $a_{n} = -K_{n,1} + 2g^2 K_{n,1} a_1 + 2g^2 K_{n,2} a_2 + 2g^2 K_{n,3} a_3 + K_{n,4} a_4 + O(g^{10})$ and that the kernel $K_{n,n'}$ can be written explicitly. This matters because the anomalous dimension is then simply $2g^2(1-a_1)$, so the whole all-orders large-spin problem becomes a matrix inversion. With that kernel the authors prove the Eden-Staudacher hypothesis: the perturbative series, written as $g^2$ times a power series in $g^2$, has coefficients that are sums of products of zeta values of maximal transcendentality, and every coefficient in front of each such product is an integer. The proof rests on showing that the combinatorial factor $T_{n,n';R}$ multiplying each zeta value is an integer, which the authors demonstrate by factoring it into a product of two binomial coefficients and a rational number whose prime content is controlled. They further show that the series has a finite radius of convergence, that the kernel has an essential singularity at $g=0$, and that the solution of the equation has an essential singularity on the second sheet of the Laplace variable $j$ at strong coupling. For the Beisert-Eden-Staudacher equation the singular solution gives $2g - 1/2 + O(1/g)$ for the anomalous dimension, reproducing the leading string-theory prediction $2^{3/2}g$.

Load-bearing premise

The strong-coupling results assume that the singular solution constructed from the small-$z$ behaviour remains valid at large $z$, and that the simplified equation obtained by replacing the analytically continued variable by the original one is a legitimate limit of the Eden-Staudacher and Beisert-Eden-Staudacher equations.

Editorial extensions

If this is right

The perturbative expansion of the large-spin anomalous dimension in N=4 super-Yang-Mills is fixed to all orders by integer-coefficient zeta products, so the series is determined once the transcendentality pattern is known.
The exact kernel gives a closed-form linear system that can be truncated and solved numerically at any coupling, providing a benchmark for weak-coupling and strong-coupling expansions.
The Beisert-Eden-Staudacher equation, which includes the crossing-symmetry phase, yields the leading string-theory prediction for the anomalous dimension at strong coupling, supporting the AdS/CFT correspondence.
The radius of convergence of the weak-coupling series is finite and located at $g^2 = -1/4$, so the perturbative series cannot be extrapolated past that point without analytic continuation.
The solution has an essential singularity on the second sheet of the Laplace variable at strong coupling, which controls the large-$j$ asymptotics and hence the approach to the large-spin limit.

Reading between the lines

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

The proof of integer coefficients is a statement about the combinatorial structure of the kernel, not about the dynamics of N=4 SYM specifically; it suggests that any equation of Eden-Staudacher type with the same kernel will have the same transcendentality property.
The discrepancy between the paper's next-to-leading strong-coupling coefficient $-1/2$ and the string-theory value $-3\pi\ln 2 \approx -0.6619$ is attributed to simplifications in the singular solution, but it may also indicate that the crossing-symmetry phase contributes at next-to-leading order in a way the simplified equation misses.
The linear system is well suited to numerical truncation, so the analytic results here can be checked against direct numerical solutions of the BES equation at intermediate coupling, where neither weak- nor strong-coupling expansions apply.

Original abstract

We investigate the Eden-Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N=4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions zeta(k) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g=infty the kernel has an essential singularity. The analytic properties of the solution of the Eden-Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert-Eden-Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

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The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We investigate the Eden-Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N=4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions zeta(k) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g=infty the kernel has an essential singularity. The analytic properties of the solution of the Eden-Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert-Eden-Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

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	We investigate the Eden-Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N=4 super-symmetric gauge theory.	contribution 0.92	0.87	0.04	asserted 0.73
s1	This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically.	method 0.97	0.83	0.03	asserted 1.00
s2	We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions zeta(k) having the property of the maximal transcendentality with the coefficients being integer numbers.	result 0.99	0.94	0.67	asserted 1.00
s3	The radius of convergency of the perturbation theory is found.	result 1.00	0.93	0.05	asserted 1.00
s4	It is shown, that at g=infty the kernel has an essential singularity.	result 1.00	0.88	0.07	asserted 1.00
s5	The analytic properties of the solution of the Eden-Staudacher equation are investigated.	contribution 0.96	0.90	0.04	asserted 0.88
s6	In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation.	result 0.99	0.91	0.13	asserted 1.00
s7	Similar results are derived also for the Beisert-Eden-Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix.	contribution 0.66	0.89	0.08	asserted 1.00
s8	We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.	result 0.94	0.91	0.32	asserted 1.00

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

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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

References

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The authors compute the full-color two-loop soft-gluon emission factor, including new non-planar tripole terms expressed in single-valued harmonic polylogarithms.

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The Collinear Limit of the Energy-Energy Correlator
hep-ph 2019-05 conditional novelty 7.0 of 10

A factorization formula for the collinear limit of the energy-energy correlator enables next-to-next-to-leading-log resummation in QCD and N=1 SYM, and reduces to a spacelike power law in N=4 SYM.
The two-loop five-point amplitude in $\mathcal N=8$ supergravity
hep-th 2019-01 accept novelty 7.0 of 10

The two-loop five-point N=8 supergravity amplitude is computed at symbol level, shown to be uniformly transcendental, and found to share most of its function space with the corresponding N=4 super-Yang-Mills amplitude.
Analytic result for a two-loop five-particle amplitude
hep-th 2018-12 accept novelty 7.0 of 10

The symbol of the two-loop five-gluon amplitude in N=4 super Yang-Mills is computed in full color, including all non-planar subleading-color terms, and expressed as permutations of Parke-Taylor tree amplitudes times p...
The two-loop five-point amplitude in $\mathcal{N} =4$ super-Yang-Mills theory
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The symbol of the two-loop five-point N=4 super-Yang-Mills amplitude is computed with full color dependence, together with the symbols of all nonplanar five-point master integrals.
Logarithmic Singularities and Maximally Supersymmetric Amplitudes
hep-th 2014-12 accept novelty 7.0 of 10

A complete three-loop four-point N=4 super-Yang-Mills integrand basis is constructed with only logarithmic singularities and no poles at infinity, and the same singularity constraints are conjectured to subsume dual c...
The three-loop form factor in N=4 super Yang-Mills
hep-th 2011-12 accept novelty 7.0 of 10

The three-loop Sudakov form factor in N=4 super Yang-Mills is computed analytically, shown to admit a uniform-transcendentality integral representation, with infrared exponentiation verified and ultraviolet behaviour ...
A Generalized Scaling Function for AdS/CFT
hep-th 2007-12 accept novelty 7.0 of 10

The authors derive a non-perturbative integral equation for a generalized scaling function f(g,j) governing twist operators in the sl(2) sector when spin and twist both grow large with their ratio to log spin fixed.
On String S-matrix, Bound States and TBA
hep-th 2007-10 accept novelty 7.0 of 10

Unitarity of the mirror S-matrix fixes the AdS5 x S5 string S-matrix essentially uniquely as a meromorphic elliptic function, with the double Wick rotation realized as a quarter-period shift on the rapidity torus.
The S-Matrix of AdS/CFT and Yangian Symmetry
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The AdS/CFT worldsheet S-matrix, already fixed by a centrally extended su(2|2) symmetry, is shown to be invariant under the corresponding Yangian with a braided coproduct.
Gravity On-shell Diagrams
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A compact Grassmannian formula reproduces gravity on-shell diagrams from edge variables, and gravity loop amplitudes appear to inherit their logarithmic-singularity and collinear-vanishing structure.
Pseudo-scalar Form Factors at Three Loops in QCD
hep-ph 2015-10 accept novelty 6.0 of 10

The three-loop massless QCD pseudo-scalar Higgs form factors are computed, and the three-loop operator mixing and finite renormalisation are independently re-derived from infrared factorization, confirming earlier OPE...
Nonsinglet pentagons and NMHV amplitudes
hep-th 2014-07 conditional novelty 6.0 of 10

Nonsinglet pentagon form factors are proposed and solved to all orders in the 't Hooft coupling, then used to reproduce twist-two contributions to NMHV hexagon amplitudes against perturbative data.
Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
hep-th 2014-07 conditional novelty 6.0 of 10

All-loop pentagon transitions for arbitrary gluon bound states are derived by fusion and checked against perturbative amplitude data up to four loops.
Quantum folded string and integrability: from finite size effects to Konishi dimension
hep-th 2011-02 conditional novelty 6.0 of 10

The Konishi operator's anomalous dimension at strong coupling is derived analytically as 2λ^{1/4} - 4 + 2/λ^{1/4}, confirming earlier numerical Y-system predictions.
Four loop twist two, BFKL, wrapping and strings
hep-th 2008-11 conditional novelty 6.0 of 10

The four-loop wrapping correction to twist-two anomalous dimensions in N=4 SYM, computed from string theory, cancels the spurious poles in the Bethe ansatz result and reproduces the LO and NLO BFKL predictions.
The Four-Loop Dressing Phase of N=4 SYM
hep-th 2007-05 accept novelty 6.0 of 10

A direct Feynman-diagram calculation in the su(2) sector of planar N=4 super Yang-Mills confirms the four-loop dressing phase coefficient beta_{2,3} = 4 zeta(3).
Two-loop world-sheet corrections in AdS_5 x S^5 superstring
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The two-loop world-sheet correction to a spinning string in AdS5 x S5 yields a2 = -(1/pi) times Catalan's constant, matching the value from the BES Bethe ansatz equation.
The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
hep-th 2006-12 accept novelty 6.0 of 10

The AdS5 x S5 string S-matrix satisfies the standard Yang-Baxter equation in a natural 'string' basis, and Beisert's gauge-theory S-matrix is the same object rewritten in a non-local basis that twists the equation.
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hep-th 2015-04 accept novelty 5.0 of 10

Two-loop minimal form factors in the SU(2) sector of planar N=4 SYM reproduce the known dilatation operator and yield new finite remainder functions whose leading transcendental part is universal.
BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
hep-th 2010-11 conditional novelty 5.0 of 10

The analytic continuation of the two-loop six-particle remainder function to the Mandelstam region reproduces the BFKL leading-log result and yields new next-to-leading impact factors and three-loop terms.
On form factors in N=4 sym
hep-th 2010-11 conditional novelty 5.0 of 10

Two-loop form factors for half-BPS operators in N=4 super Yang-Mills exponentiate their infrared divergences with a universal cusp anomalous dimension and a process-dependent collinear anomalous dimension.
Quantum integrability and functional equations
hep-th 2010-03 conditional novelty 4.0 of 10

The thesis recasts integral Bethe Ansatz equations as Riemann-Hilbert and functional equations, then uses them to check the AdS/CFT asymptotic Bethe Ansatz at strong coupling and to solve its crossing equations.
Strong-coupling expansion of cusp anomaly from quantum superstring
hep-th 2007-09 accept novelty 4.0 of 10

The two-loop coefficient of the cusp anomalous dimension's strong-coupling expansion is minus the Catalan constant, confirming the Bethe-ansatz prediction and the cancellation of two-loop divergences.
DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
hep-th 2019-08 unverdicted

A review of known results on DGLAP and BFKL equations in N=4 SYM, from weak-coupling perturbation theory to strong coupling via AdS/CFT and integrability, with no new derivations.

How the literature uses it

44 arXiv papers cite this in 59 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 · 43 sentences without a confident label

Uses its data or values 1 paper

By the maximal-transcendentality principle [ref] , the $w=4$ terms in the coefficients of $C_A^4$ and $d_AA^(4)/n_a$ may be gleaned respectively from the planar [ref] and nonplanar [ref] universal anomalous dimensions of the twist-two operators with general Lorentz spin $N$ at N$^3$LO in $𝒩=4$ SYM, which serves as welcome input.

Four-Loop Gluon Anomalous Dimension of General Lorentz Spin: Transcendental Part · Introduction · 0.80

Compares with it 1 paper

In particular the $ℓ=0$ result obtained in this order of limits coincides with the solution obtained [ref] via the BES equation [ref] , which supposes $J=2$ and $S$ large and then $g→∞$.

Quantum folded string and integrability: from finite size effects to Konishi dimension · Introduction · 0.96

Cites it as background 12 papers

The principle of maximal transcendentality (PMT) [ref] establishes a bridge between the results in QCD and those of $N=4$ SYM which are comparatively simpler.

The Curious Case of Leading Transcendentality: Three Point Form Factors · Principle of maximal transcendentality and its violation · 0.99
Using the supersymmetric extensions of Balitskii-Fadin-Kuraev-Lipatov (BFKL) [ref] and DGLAP [ref] evolution equations, Kotikov and Lipatov [ref] conjectured leading transcendentality (LT) principle which states that the eigenvalues of anomalous dimension [ref] matrix of twist two composite operators made out of $λ$, $g$ and complex $ϕ$ fields in $N=4$ SYM theory contain uniform transcendental terms at every order in perturbation theory.

Infrared structure of $\mathcal{N}$ = 4 SYM and leading transcendentality principle in gauge theory · Analytical results and discussion · 0.88
Using the supersymmetric extensions of Balitskii-Fadin-Kuraev-Lipatov (BFKL) [ref] and DGLAP [ref] evolution equations, Kotikov and Lipatov [ref] conjectured leading transcendentality (LT) principle which states that the eigenvalues of anomalous dimension [ref] matrix of twist two composite operators made out of $λ$, $g$ and complex $ϕ$ fields in $N=4$ SYM theory contain uniform transcendental terms at every order in perturbation theory.

Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory · Analytical results and discussion · 0.84

Discussion

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