Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT

Eden, Burkhard; Petkou, Anastasios C.; Schubert, Christian; Sokatchev, E.

doi:10.1016/s0550-3213(01)00151-1

Cited by 184 publications

(343 citation statements)

References 60 publications

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“…Again conformal transformations can be used to justify the appearance of the 2-variable function Φ (2) . The r.h.s.…”

Section: Jhep01(2007)064mentioning

confidence: 99%

“…It has been found that their form is more restricted than would follow from just superconformal kinematics. This property, called 'partial non-renormalisation' in [2] is observed in the perturbative one-loop [3] and two-loop [4] CFT calculations, as well as in their AdS supergravity (or strong coupling) dual [5]. These explicit results have been analysed through OPE methods [6] and the twoloop anomalous dimensions of all twist two operators in the theory were found in [7].…”

Section: Introductionmentioning

confidence: 99%

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Magic identities for conformal four-point integrals

Drummond¹,

Henn²,

Smirnov³

et al. 2007

J. High Energy Phys.

465

912

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Abstract:We propose an iterative procedure for constructing classes of off-shell fourpoint conformal integrals which are identical. The proof of the identity is based on the conformal properties of a subintegral common for the whole class. The simplest example are the so-called 'triple scalar box' and 'tennis court' integrals. In this case we also give an independent proof using the method of Mellin-Barnes representation which can be applied in a similar way for general off-shell Feynman integrals.

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“…Again conformal transformations can be used to justify the appearance of the 2-variable function Φ (2) . The r.h.s.…”

Section: Jhep01(2007)064mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magic identities for conformal four-point integrals

Drummond¹,

Henn²,

Smirnov³

et al. 2007

J. High Energy Phys.

465

912

View full text Add to dashboard Cite

show abstract

“…As the first non-trivial objects the four-point functions have been intensely studied both at weak coupling in field theory perturbation theory and at strong coupling exploiting the AdS/CFT duality. The loop corrections to these four-point function take a factorised form [47]:…”

Section: Jhep01(2015)116mentioning

confidence: 99%

“…(2.4) According to [47][48][49][50][51][52][53][54] the Born level correlator with maximum k = n − 4 (maximally nilpotent piece) has the form → 0 which we are interested in. The objects f ( ) (x 1 , .…”

Section: Jhep01(2015)116mentioning

confidence: 99%

Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

Ambrosio

Eden

Goddard

et al. 2015

J. High Energ. Phys.

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Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs.By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops.All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops.Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four-to five-point amplitudes.

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“…On the field theory side, the integrand of the four-point function of stress-tensor multiplets has been elaborated in [8,[14][15][16] up to eight loops. It takes the form of a kinematic factor [17] times a sum of scalar conformal integrals in a propagator representation. At four loops (and beyond), the largest part of the integrals has not yet been evaluated: there are 26 genuine four-loop integrals in the planar part of the correlator (so the part relevant to integrability), of which five can be related to the ladder with four rungs by flip identities on subintegrals.…”

Section: Introductionmentioning

confidence: 99%

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

Eden

Smirnov

2016

J. High Energ. Phys.

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We evaluate a four-loop conformal integral, i.e. an integral over four fourdimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

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Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT

Cited by 184 publications

References 60 publications

Magic identities for conformal four-point integrals

Magic identities for conformal four-point integrals

Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

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

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