Superconformal operators in N=4 super-Yang-Mills theory

A.N. Manashov; A.V. Belitsky; G.P. Korchemsky; S.E. Derkachov

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Superconformal operators in N=4 super-Yang-Mills theory

A.V. Belitsky, S.E. Derkachov, G.P. Korchemsky, A.N. Manashov

High Energy Physics - Theory · Submitted 12 Nov 2003

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

The authors' main claim In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.

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arXiv IDhep-th/0311104 (version 4)

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CitationA.N. Manashov, A.V. Belitsky, G.P. Korchemsky, S.E. Derkachov. "Superconformal operators in N=4 super-Yang-Mills theory." arXiv:hep-th/0311104 (2003). https://pith.science/paper/RN42KTY6

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.69 · mentions code or data availability 0.01.

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We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators. The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built. A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet. Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties.	contribution 1.00	0.95	0.20	asserted 1.00
s1	The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators.	result 0.96	0.76	0.15	asserted 1.00
s2	The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built.	background 0.60	0.25	0.08	asserted 1.00
s3	A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet.	result 0.72	0.45	0.23	asserted 1.00
s4	Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry.	background 0.98	0.09	0.06	asserted 1.00
s5	In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2\|4) Heisenberg spin chain.	result 0.96	0.70	0.58	asserted 1.00

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Original abstract

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators. The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built. A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet. Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.

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Cited by 11 Pith papers

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The energy-energy correlation in both end-point regions is expressed as a compact function of twist-two conformal data, reproducing known NNLO results and predicting the next order.
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Permutation symmetry plus light-cone and short-distance constraints fix the planar four-point correlator integrand in N=4 SYM through six loops, matching the known six-loop four-particle amplitude.

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26 arXiv papers cite this in 49 sentences

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Papers citing it · 38 sentences without a confident label

Uses its data or values 1 paper

The eigenvalues of $γ_0$ for $𝒪_s = S^(1),S^(2),S̃^(1),S̃^(2),M_s,M̅_s$ read [ref] : [equation] with: [equation] and [ref] : [equation] Besides [ref] : [equation] We have verified that the first $10^4$ eigenvalues of $γ_0/β_0$ are nonresonant, with $β_0 =3/(4π)^2$.

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I · Anomalous dimensions of twist-$2$ operators in $𝒩 = 1$ SUSY YM theory · 0.94

Compares with it 1 paper

The corresponding primary conformal operators match precisely the ones in [ref] up to perhaps the overall normalization: [equation] with $j = s+1$, $l =s-2$ and $α= 5/2$.

$n$-point correlators of twist-$2$ operators in $SU(N)$ Yang-Mills theory to the lowest perturbative order · Standard basis · 0.98

Cites it as background 8 papers

In the following, we will focus on a second particularly interesting class of operators, the so-called quasipartonic twist operators [ref] .

QCD-like properties for anomalous dimensions in N=4 SYM · Introduction and conclusions · 0.91
This part of the appendix will review the Grassmann and harmonic variables needed for representing the planar four-point correlator in $𝒩=4$ SYM using the following references [ref] .

Perturbative Correlation Functions and Scattering Amplitudes in Planar $\mathcal{N}=4$ Supersymmetric Yang-Mills · Grassmann and Harmonic Variables · 0.91
Let us consider the super-multiplet of local operators [ref] defined as [ref]

Pseudo and quasi gluon PDF in the BFKL approximation · Super-multiplet of local operators in CFT · 0.89

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