Finite remainders of the Konishi at two loops in ${\cal N}=4$ SYM

Maguni Mahakhud; Prasanna K. Dhani; Pulak Banerjee; Satyajit Seth; V. Ravindran

RECORD

Finite remainders of the Konishi at two loops in ${\cal N}=4$ SYM

Pulak Banerjee, Prasanna K. Dhani, Maguni Mahakhud, V. Ravindran, Satyajit Seth

High Energy Physics - Theory · Submitted 2 Dec 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1612.00885 (version 2)

Pith IDNTILM62X, Pith's permanent record of this paper and its review

CitationMaguni Mahakhud, Prasanna K. Dhani, Pulak Banerjee, Satyajit Seth, V. Ravindran. "Finite remainders of the Konishi at two loops in ${\cal N}=4$ SYM." arXiv:1612.00885 (2016). https://pith.science/paper/NTILM62X

Claim paper

The compiled record

The paper's own sentences, arranged. 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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,044 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.55 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of $g \phi \phi$ and $\phi \lambda \lambda$, where $\phi,\lambda, g$ are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for $g \phi \phi$ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

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 present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach.	contribution 1.00	0.96	0.08	asserted 1.00
s1	We have chosen on shell final states consisting of $g \phi \phi$ and $\phi \lambda \lambda$, where $\phi,\lambda, g$ are scalar, Majorana fermion and gauge fields respectively.	method 0.94	0.89	0.02	asserted 0.99
s2	The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme.	method 1.00	0.93	0.02	asserted 1.00
s3	We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators.	method 0.74	0.93	0.04	asserted 1.00
s4	Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them.	method 0.95	0.95	0.15	asserted 1.00
s5	We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively.	result 1.00	0.97	0.26	asserted 1.00
s6	In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality.	result 1.00	0.94	0.29	asserted 1.00
s7	However, surprisingly, the leading transcendental terms for $g \phi \phi$ agree with that of the half-BPS.	result 0.99	0.93	0.18	asserted 1.00
s8	We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.	interpretation 0.80	0.92	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.68.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

The paper

Original abstract

We present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of $g \phi \phi$ and $\phi \lambda \lambda$, where $\phi,\lambda, g$ are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for $g \phi \phi$ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

An Operator Product Expansion for Form Factors
hep-th 2020-09 conditional novelty 8.0 of 10

A new operator product expansion for planar form factors in N=4 SYM is introduced, built on a novel form factor transition that matches known one- and two-loop results and predicts higher orders.
Universal and Transcendental Structures in Protected ABJM Two-Point Functions
hep-th 2026-08 accept novelty 7.0 of 10

The two-loop correction to any protected two-point function in ABJM theory is given by a formula involving the tree-level metric and a kernel connecting Young diagrams differing by one box.
A Three-Point Form Factor Through Five Loops
hep-th 2020-12 conditional novelty 7.0 of 10

The three-point MHV form factor of the stress-tensor supermultiplet in planar N=4 super-Yang-Mills is fixed through five loops by a symbol bootstrap with new adjacency and multiple-final-entry constraints.
The Sudakov form factor at four loops in maximal super Yang-Mills theory
hep-th 2017-11 accept novelty 7.0 of 10

The four-loop nonplanar cusp anomalous dimension in N=4 super Yang-Mills is nonzero, explicitly violating the conjectured quadratic Casimir scaling of infrared divergences.
$\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
hep-th 2018-04 conditional novelty 6.0 of 10

Two-loop form factors of Tr(F^3) and its Konishi-descendant supersymmetric completion in N=4 super Yang-Mills are computed for three gluons and shown to exhibit maximal transcendentality.

Show 2 more citing papers

Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory
hep-th 2017-07 conditional novelty 6.0 of 10

The maximally transcendental part of the two-loop Tr F^3 form factor with three gluons equals the form factor of the protected operator T3 in N=4 SYM, and this part is argued to be universal across theories including QCD.
Tracing Transcendentality in Protected Correlators of N=4 SYM
hep-th 2026-06 unverdicted novelty 5.0 of 10

Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.

How the literature uses it

25 arXiv papers cite this in 47 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 · 37 sentences without a confident label

Compares with it 4 papers

Moreover, the results are exactly same as that of the half-BPS operator [ref] which is presented explicitly in terms of MPLs in appendix [ref].

The Curious Case of Leading Transcendentality: Three Point Form Factors · Principle of uniform transcendentality · 0.83
The same $R^(2)_len-2;4$ function was also obtained in Konishi form factor in $N=4$ SYM [ref] .

Hidden Analytic Structure of Higgs Amplitudes and Maximal Transcendentality Principle · Analytic results and hidden structures · 0.85
The same function was also obtained in the non-BPS Konishi form factor in $N=4$ SYM [ref] .

Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD · Maximal Transcendentality Principle: Length-2 Cases · 0.82

Cites it as support 2 papers

This provides further support of the maximal transcendentality principle introduced in study of anomalous dimensions in [ref] and then observed for the form factor of $tr(F^2)$ in [ref] and later also for other operators [ref] .

Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes · Introduction · 0.99
Many evidences from form factor results at two loops [ref] support the intriguing maximal transcendentality principle (MTP) [ref] which conjectures that $𝒩=4$ SYM captures the maximally transcendental part of QCD.

Full-color three-loop three-point form factors in N=4 SYM · Introduction · 0.96

Cites it as background 4 papers

In four-dimensional $𝒩=4$ super-Yang-Mills (SYM) theory scattering amplitudes [ref] , Wilson loops [ref] , and form factors [ref] often exhibit uniform transcendentality, a feature conjecturally tied to the underlying integrable structure of the theory [ref] .

Uniformly transcendental bases for protected two-point functions · Introduction · 0.80
The two-loop three-point FF and their finite remainders for the half-BPS [ref] and the Konishi operator were recently calculated in [ref] .

Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory · Introduction · 0.89
Uniform transcendentality has also been observed extensively in scattering amplitudes [ref] , light-like Wilson loops [ref] , and form factors of local operators [ref] .

Universal and Transcendental Structures in Protected ABJM Two-Point Functions · Introduction · 0.87

What it cites · 83 sentences without a confident label

Builds on 6 papers

Later it was extended to cases with more than two external states [ref] .

Analytic two-loop form factors in N=4 SYM · Finite Remainders · 0.83
Later it was extended to cases with more than two external states [ref] .

The last of the simple remainders · Finite Remainders · 0.83
The generalisation of the results in [ref] and [ref] for all loop in $SU(N)$ gauge theory having $n_f$ light flavours in terms of cusp, collinear and soft anomalous dimensions was formulated by Becher and Neubert [ref] and independently by Gardi and Magnea [ref] .

Infrared singularities of scattering amplitudes in perturbative QCD · Introduction · 0.88

Uses the method or tool of 8 papers

We used analog of KG that QCD form factors satisfy [ref] to determine the anomalous dimension $γ^ρ$.

Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond · UV divergences · 0.98
Using the fortran routines of Gehrmann and Remiddi [ref] we have compared the finite remainder of the half-BPS operator presented in eq.

Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms · Finite Remainders · 0.98
Using Reduze [ref] , the loop momenta in various integrals can be shifted suitably in order to belong to these sets.

Reduze 2 - Distributed Feynman Integral Reduction · Methodology of calculation · 1.00

Compares with 2 papers

(4.32) of [ref] ) and found excellent agreement within the numerical accuracy.

Analytic two-loop form factors in N=4 SYM · Finite Remainders · 1.00
The anomalous dimension up to 2-loop are in agreement with the existing ones [ref] .

Three-Loop Four-Point Correlator in N=4 SYM · UV divergences · 0.99

Cites as background 47 papers

Over the last few years, there are several results [ref] on n-point FFs for the Konishi operator in the weak coupling limit of $N=4$ SYM.

Two-Loop SL(2) Form Factors and Maximal Transcendentality · Introduction · 0.99
Over the last few years, there are several results [ref] on n-point FFs for the Konishi operator in the weak coupling limit of $N=4$ SYM.

On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders · Introduction · 0.99
Over the last few years, there are several results [ref] on n-point FFs for the Konishi operator in the weak coupling limit of $N=4$ SYM.

The SU(2|3) dynamic two-loop form factors · Introduction · 0.99

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.