Glue-and-cut at five loops

Georgoudis, Alessandro; Gonçalves, Vasco; Panzer, Erik; Pereira, Raul; Smirnov, Alexander V.; Smirnov, Vladimir A.

doi:10.1007/jhep09(2021)098

Cited by 18 publications

(9 citation statements)

References 58 publications

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“…Furthermore, these types of Feynman integral periods have been studied in the literature (see e.g. [26][27][28][29][30][31][32][33]),…”

Section: Integrated Correlators and Feynman Graph Periodsmentioning

confidence: 99%

“…The observation of this paper is that, instead of taking the analytical results of the un-integrated correlator, it is much more convenient to simply use the loop integrands of the correlator. When integrated with the integration measures that are used in the definition of the integrated correlators, the graphs representing the loop integrands of the un-integrated correlator become precisely the periods of certain Feynman graphs with vertices of degree-(−4), and such periods have been studied quite extensively in the literature, see for example [26][27][28][29][30][31][32][33]. In particular, for the first integrated correlator at L loops, it involves the computation of (L + 1)-loop periods; for the second integrated correlator at L loops, it is given by a sum of (L + 2)-loop periods.…”

Section: Introductionmentioning

confidence: 99%

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Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods

Wen,

Zhang

2022

Preprint

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We study perturbative aspects of recently proposed integrated four-point correlators in N = 4 supersymmetric Yang-Mills with all classical gauge groups using standard Feynman diagram computations. We argue that perturbative contributions of the integrated correlators are given by linear combinations of periods of certain conformal Feynman graphs, which were originally introduced for the construction of perturbative loop integrands of the un-integrated correlator. This observation allows us to evaluate the integrated correlators to high loop orders. We explicitly compute one of the integrated correlators up to four loops in the planar limit, and up to three loops for the other integrated correlator, and find agreement with the results obtained from supersymmetric localisation. The identification between the integrated correlators and certain periods also implies non-trivial relations among these periods, given that one may compute the integrated correlators using localisation. We illustrate this idea by considering one of the integrated correlators at five loops in the planar limit, where the localisation result leads to a prediction for the period of a certain six-loop integral.

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“…Furthermore, these types of Feynman integral periods have been studied in the literature (see e.g. [26][27][28][29][30][31][32][33]),…”

Section: Integrated Correlators and Feynman Graph Periodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods

Wen,

Zhang

2022

Preprint

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“…The lower loop sub IR divergences take much less time to evaluate compared with IBP. Moreover, the analytic expressions of L-loop vacuum integrals with a single massive propagators can be easily obtained from (L − 1)-loop massless propagator integrals, for which the analytic expressions are known to 5 loops [29][30][31][32][33].…”

Section: Ir Regulation By Adding Two Massesmentioning

confidence: 99%

The Decomposition of UV Divergence

Jin¹

2022

Preprint

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We present an efficient algorithm to decompose the ultraviolet (UV) divergences of Feynman integrals to local divergences and various types of sub-divergences. We show that with some reasonable assumptions the local divergences of Feynman integrals can be uniquely defined in dimensional regularization scheme. By an asymptotic expansion in the hard momenta, the computation of local and sub-divergences is reduced to the computation of local divergences of massless vacuum integrals. In theories with spin ≤ 1 2 , the beta functions and anomalous dimensions can be extracted directly from the local divergence of integrals.We also propose two methods to reduce the tensor structures which can be used in the computation of local divergence. The first method is based on dimensional shift and is extremely powerful for integrals with loop number L ≤ 3. The second method is based on a PV reduction in a d ∞ dimension subspace, and it is more suited in four and more loops.

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“…All the Feynman integrals that contribute to eq. (7.26) are massless two-point functions, also called p-integrals [74][75][76][77], which we computed with the code Forcer [78]. In order to renormalise eq.…”

Section: Renormalisation Of Physical Operatorsmentioning

confidence: 99%

Renormalization of gluonic leading-twist Operators in covariant Gauges

Falcioni,

Herzog

2022

Preprint

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We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green's functions with insertions of twist-two operators in Yang-Mills theory. Using this structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator from a single exact operator in the BRST-generalised sense. We show that our construction complies with the theorems by Joglekar and Lee. We further establish the existence of a generalised anti-BRST symmetry which we employ to derive non-trivial relations among the anomalous dimension matrices of ghost and equation-of-motion operators. For the purpose of demonstration we employ the formalism to compute the N = 2, 4 Mellin moments of the gluonic splitting function up to 4 loops and its N = 6 Mellin moment up to 3 loops, where we also take advantage of additional simplifications of the background field formalism.

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Glue-and-cut at five loops

Cited by 18 publications

References 58 publications

Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods

Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods

The Decomposition of UV Divergence

Renormalization of gluonic leading-twist Operators in covariant Gauges

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