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Five-loop anomalous dimension at critical wrapping order in N=4 SYM
High Energy Physics - Theory · Submitted 3 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our result from perturbation theory confirms explicitly the formula conjectured in arXiv:0901.4864 for the five-loop anomalous dimension of twist-three operators.
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The abstract, sentence by sentence
We compute the anomalous dimension of a length-five operator at five-loop order in the SU(2) sector of N=4 SYM theory in the planar limit. This is critical wrapping order at five loops. The result is obtained perturbatively by means of N=1 superspace techniques. Our result from perturbation theory confirms explicitly the formula conjectured in arXiv:0901.4864 for the five-loop anomalous dimension of twist-three operators. We also explicitly obtain the same result by employing the recently proposed Y-system.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We compute the anomalous dimension of a length-five operator at five-loop order in the SU(2) sector of N=4 SYM theory in the planar limit. | contribution 0.99 | 0.97 | 0.17 | asserted 1.00 |
| s1 | This is critical wrapping order at five loops. | interpretation 0.46 | 0.43 | 0.10 | asserted 1.00 |
| s2 | The result is obtained perturbatively by means of N=1 superspace techniques. | method 1.00 | 0.89 | 0.03 | asserted 1.00 |
| s3 | Our result from perturbation theory confirms explicitly the formula conjectured in arXiv:0901.4864 for the five-loop anomalous dimension of twist-three operators. | result 0.79 | 0.82 | 0.46 | asserted 1.00 |
| s4 | We also explicitly obtain the same result by employing the recently proposed Y-system. | method 0.49 | 0.95 | 0.12 | asserted 1.00 |
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The paper
Original abstract
We compute the anomalous dimension of a length-five operator at five-loop order in the SU(2) sector of N=4 SYM theory in the planar limit. This is critical wrapping order at five loops. The result is obtained perturbatively by means of N=1 superspace techniques. Our result from perturbation theory confirms explicitly the formula conjectured in arXiv:0901.4864 for the five-loop anomalous dimension of twist-three operators. We also explicitly obtain the same result by employing the recently proposed Y-system.
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References
How the literature uses it
20 arXiv papers cite this in 38 sentences
Papers citing it · 35 sentences without a confident label
Uses its method or tool 1 paper
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This method is particularly effective in our case because the insertion of the composite operator, being a vertex from where a large number of lines start, is typically a very good candidate for the root vertex [ref] , whose wise choice can simplify the calculation considerably.
Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM · The four-loop case · 1.00
Compares with it 1 paper
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Moreover, it agrees [ref] with the prediction of the Y-system, thus representing a new independent check for it.
Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM · The five-loop case · 0.89
Cites it as background 1 paper
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On the one hand, a generalized Lüscher approach for treating the leading wrapping effects was developed [ref] and successfully confronted against direct field-theoretic computations [ref] .
On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra · Introduction · 0.86
What it cites · 26 sentences without a confident label
Builds on 2 papers
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To compute the leading wrapping correction to the anomalous dimension, we extend to five loops the explicit computation of [ref] for the four-loop case.
Integrability for the Full Spectrum of Planar AdS/CFT · Computation with the Y-system · 0.99
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In this paper we have computed perturbatively the planar anomalous dimension of a length-five operator at five loops by extending the procedure of our paper [ref] .
Anomalous dimension with wrapping at four loops in N=4 SYM · Concluding remarks · 0.98
Uses the method or tool of 5 papers
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As already mentioned, the strategy which we adopt here is the same as the one used in our previous papers [ref] .
Wrapping at four loops in N=4 SYM · Computation of the anomalous dimension at five loops · 0.98
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As already mentioned, the strategy which we adopt here is the same as the one used in our previous papers [ref] .
Anomalous dimension with wrapping at four loops in N=4 SYM · Computation of the anomalous dimension at five loops · 0.98
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Using the expression for $Y_a,0^*(u)$, the leading wrapping contribution to the anomalous dimension can be found with the help of the formula [ref] [equation] At the lowest order in $λ$, we find [equation] Moreover, since $Y_a,0^*(u)∼λ^L+2$, we can approximate $log[1+Y_a,0^*(u)]= Y_a,0^*(u)+o(λ^L+2)$, so that at leading order we have [equation] The integral can now be computed by using the residue method, closing the integration path at infinity in the upper half of the complex plane.
Integrability for the Full Spectrum of Planar AdS/CFT · Computation with the Y-system · 0.98
Uses data or values from 1 paper
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Using the values given in appendix [ref], we find [equation] The $β_2,3,3$ component of the dressing phase is known to be equal to $4ζ(3)$ [ref] , while for $β_2,3,4$ we use the value $-40ζ(5)$ conjectured in [ref] .
The Four-Loop Dressing Phase of N=4 SYM · Subtraction of range-six diagrams from the asymptotic dilatation operator · 1.00
Compares with 4 papers
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Our result matches the prediction of [ref] , thus providing a confirmation from perturbative field theory of the general formulas proposed there.
Twist-three at five loops, Bethe Ansatz and wrapping · Introduction · 0.96
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Moreover, we have explicitly shown that our result agrees with the one obtained by applying the Y-system proposed in [ref] .
Integrability for the Full Spectrum of Planar AdS/CFT · Concluding remarks · 0.99
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Moreover, we have explicitly shown that our result agrees with the one obtained by applying the Y-system proposed in [ref] .
Integrability for the Full Spectrum of Planar AdS/CFT II · Concluding remarks · 0.99
Cites as background 13 papers
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One of them is based on a generalization of Lüscher formula [ref] , while others are based on the Y-system [ref] and on the thermodynamic Bethe ansatz [ref] .
Wrapping interactions at strong coupling -- the giant magnon · Introduction · 0.90
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One of them is based on a generalization of Lüscher formula [ref] , while others are based on the Y-system [ref] and on the thermodynamic Bethe ansatz [ref] .
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states · Introduction · 0.90
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One of them is based on a generalization of Lüscher formula [ref] , while others are based on the Y-system [ref] and on the thermodynamic Bethe ansatz [ref] .
Finite-Size Effects for Multi-Magnon States · Introduction · 0.90
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