Half-BPS half-BPS twist two at four loops in N=4 SYM

Burkhard Eden; Felix Paul

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Half-BPS half-BPS twist two at four loops in N=4 SYM

Burkhard Eden, Felix Paul

High Energy Physics - Theory · Submitted 15 Aug 2016

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

The authors' main claim The OPE limit of the stress tensor four-point function allows us to extract the (square of the) three-point couplings between two stress tensor multiplets and one twist two operator in the 20' of SU(4).

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.45 · mentions code or data availability 0.05.

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We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly known only up to three loops. Fortunately, the double coincidence limit of the four-loop integrals can be found by the method of expansion by regions, which reduces the problem of computing the four-point integrals to the evaluation of a large set of massless propagator integrals. These can in turn be evaluated by IBP reduction. The OPE limit of the stress tensor four-point function allows us to extract the (square of the) three-point couplings between two stress tensor multiplets and one twist two operator in the 20' of SU(4). The latest available IBP software accomplishes this task up to and including spin 8. With the data obtained we hope to further the development of the recent integrable systems picture for correlation functions.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory.	contribution 0.76	0.65	0.04	asserted 0.84
s1	Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly known only up to three loops.	gap 0.93	0.07	0.03	asserted 1.00
s2	Fortunately, the double coincidence limit of the four-loop integrals can be found by the method of expansion by regions, which reduces the problem of computing the four-point integrals to the evaluation of a large set of massless propagator integrals.	method 0.97	0.45	0.08	asserted 0.94
s3	These can in turn be evaluated by IBP reduction.	method 1.00	0.27	0.03	asserted 0.96
s4	The OPE limit of the stress tensor four-point function allows us to extract the (square of the) three-point couplings between two stress tensor multiplets and one twist two operator in the 20' of SU(4).	contribution 0.32	0.57	0.36	asserted 0.94
s5	The latest available IBP software accomplishes this task up to and including spin 8.	limitation 0.92	0.14	0.04	asserted 0.97
s6	With the data obtained we hope to further the development of the recent integrable systems picture for correlation functions.	future work 0.99	0.09	0.08	hedged possibility 0.76

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from simulation or computation 0.60.

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The paper

Original abstract

We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly known only up to three loops. Fortunately, the double coincidence limit of the four-loop integrals can be found by the method of expansion by regions, which reduces the problem of computing the four-point integrals to the evaluation of a large set of massless propagator integrals. These can in turn be evaluated by IBP reduction. The OPE limit of the stress tensor four-point function allows us to extract the (square of the) three-point couplings between two stress tensor multiplets and one twist two operator in the 20' of SU(4). The latest available IBP software accomplishes this task up to and including spin 8. With the data obtained we hope to further the development of the recent integrable systems picture for correlation functions.

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References

Forward citations

Cited by 3 Pith papers

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

Energy correlations in the end-point region
hep-th 2019-05 conditional novelty 7.0 of 10

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.
Bootstrapping Holographic Theories in the Planar Limit
hep-th 2026-09 conditional novelty 6.0 of 10

Bootstrap plus localization, with no integrability input, reproduces single-trace operator dimension bounds that match independent predictions in planar N=4 SYM and in an N=2 open-string dual.
Structure constants at wrapping order
hep-th 2017-02 conditional novelty 6.0 of 10

A renormalization procedure tames wrapping-order divergences in the hexagon approach to structure constants, yielding a Luscher-type formula that reproduces the four-loop Konishi OPE coefficient.

How the literature uses it

14 arXiv papers cite this in 19 sentences

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Papers citing it · 14 sentences without a confident label

Uses its data or values 2 papers

In particular, we obtain [equation] while the lower loop $F^(n)$ were computed in [ref] .

Konishi OPE coefficient at the five loop order · From integrals to conformal data · 0.80
This OPE coefficient is currently known through four loops [ref] (see [ref] for the earlier loop orders) (C^∙∘∘/C^∘∘∘)^2 = 1/6-2g^2+(28+12ζ_3)g^4-(384+64ζ_3+200ζ_5)g^6 + (4976+656ζ_3+1960ζ_5+144ζ_3^2+2940ζ_7)g^8 + O(g^10) , where $g^2 = λ/(4π)^2$ is the 't Hooft coupling and $ζ_z = ζ(z)$ is the Riemann zeta function.

Structure constants at wrapping order · Introduction · 0.91

Compares with it 1 paper

At weak coupling, we found that our upper bounds are close to being saturated by the four-loop weak coupling estimates [ref] for a remarkably large range of couplings.

Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold · Discussion · 0.99

Cites it as background 2 papers

There are calculations of the structure constants of two protected operators and a twist-two operator, the most recent performed using the hexagon approach [ref] up to the four-loop [ref] and five-loop [ref] level.

Structure constants of twist-two light-ray operators in the triple Regge limit · Introduction · 0.92
Indeed, for any gauge group $G$, perturbatively at small $g_YM$ one can calculate various observables using Feynman diagrams—see, for instance, [ref] for cutting-edge results at four loops.

Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold · Introduction and Summary · 0.91

What it cites · 28 sentences without a confident label

Contests 1 paper

The principal motivation for this study is a problem with the hexagon proposal [ref] that can be probed and hopefully mended using the structure constants that we elaborate here: the proposal contains the integration over the rapidity of virtual excitations.

Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory · Introduction · contest 0.71

Builds on 1 paper

The results of this paper confirm and extend the analysis of [ref] .

Extracting OPE coefficient of Konishi at four loops · Introduction · 0.90

Uses the method or tool of 9 papers

We employed the programs FIRE5 [ref] and LiteRed [ref] for the reduction.

FIRE5: a C++ implementation of Feynman Integral REduction · Introduction · 1.00
We employed the programs FIRE5 [ref] and LiteRed [ref] for the reduction.

Presenting LiteRed: a tool for the Loop InTEgrals REDuction · Introduction · 1.00
In [ref] the differential equations method for master integrals of uniform transcendentality weight [ref] was applied in this context, for reasons of simplicity and comparability to begin with on a linearly reducible test case.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations · Introduction · 0.82

Compares with 3 papers

We find for the four-loop anomalous dimensions [equation] in full agreement with the integrability prediction in the literature [ref] .

Four loop twist two, BFKL, wrapping and strings · Waves and Conclusions · 0.98
We find for the four-loop anomalous dimensions [equation] in full agreement with the integrability prediction in the literature [ref] .

Dressing and Wrapping · Waves and Conclusions · 0.98
Our analysis confirms the result of [ref] for $α_4(2)$, which is in itself a valuable piece of information because the calculation is large enough to offer space for errors.

Extracting OPE coefficient of Konishi at four loops · Waves and Conclusions · 0.98

Cites as background 3 papers

Some ten years after the discovery of the integrability of the spectrum problem the “hexagon proposal” for computing three-point functions has been formulated in the recent breakthrough publication [ref] .

Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory · Introduction · 0.92
Another recent discovery is an integrable system for the so-called remainder function in planar scattering amplitudes [ref] .

Space-time S-matrix and Flux-tube S-matrix at Finite Coupling · Introduction · 0.98
Another recent discovery is an integrable system for the so-called remainder function in planar scattering amplitudes [ref] .

Thermodynamic Bubble Ansatz · Introduction · 0.98

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