New dual conformally invariant off-shell integrals

Nguyen, Dung Xuan; Spradlin, Marcus; Volovich, Anastasia

doi:10.1103/physrevd.77.025018

Cited by 35 publications

(27 citation statements)

References 35 publications

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“…Secondly, the gluon amplitudes have the intriguing property of 'dual' conformal symmetry [25] (see also [9,44]). All the scalar Feynman integrals appearing in the calculations of Bern et al up to four loops 20 are dual to conformal integrals, after we take them off shell and perform the change of variables (6) from momenta to 'dual coordinates'.…”

Section: Discussionmentioning

confidence: 99%

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Drummond¹,

Henn²,

Korchemsky³

et al. 2010

Nuclear Physics B

346

660

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Planar gluon amplitudes in N = 4 SYM are remarkably similar to expectation values of Wilson loops made of light-like segments. We argue that the latter can be determined by making use of the conformal symmetry of the gauge theory, broken by cusp anomalies. We derive the corresponding anomalous conformal Ward identities valid to all loops and show that they uniquely fix the form of the finite part of a Wilson loop with n cusps (up to an additive constant) for n = 4 and 5 and reduce the freedom in it to a function of conformal invariants for n ≥ 6. We also present an explicit two-loop calculation for n = 5. The result confirms the form predicted by the Ward identities and matches the finite part of the two-loop five-gluon planar MHV amplitude, up to a constant. This constitutes another non-trivial test of the Wilson loop/gluon amplitude duality.

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Section: Discussionmentioning

confidence: 99%

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Drummond¹,

Henn²,

Korchemsky³

et al. 2010

Nuclear Physics B

346

660

View full text Add to dashboard Cite

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“…Similar representations can be derived also for the 4-point functions, (see e.g. [10] for the case L = 3). Let us stress that, although all the propagators are massless, since in general x 2 ij = 0, one has to compute these "momentum space like" integrals with off-shell external legs.…”

Section: Alternative Representations Of G Lmentioning

confidence: 86%

“…(12) has been considered, in a particular kinematical regime appropriate for taking the on-shell limit, in [10] where also a MellinBarnes representation has been derived. Before proceeding to the proof in the case of general L, we list the expressions for the simpler cases of L = 1 …”

Section: Introductionmentioning

confidence: 99%

The massless supersymmetric ladder with L rungs

Rossi

Stanev

2009

Nuclear Physics B

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We show that in the massless N = 1 supersymmetric Wess-Zumino theory it is possible to devise a computational strategy by which the x-space calculation of the ladder 4-point correlators can be carried out without introducing any regularization. As an application we derive a representation valid at all loop orders in terms of conformal invariant integrals. We obtain an explicit expression of the 3-loop ladder diagram for collinear external points. † Giancarlo.Rossi@roma2.infn.it ‡ Yassen.Stanev@roma2.infn.it

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“…The divergent part of the integral over y 1 is thus 18) and the remaining integral over y 2 diverges whenever λ j (y 2 ) = λ k (y 2 ), i.e., when y 2 is a root of the discriminant discrim y 1 (G). It is also clear that these roots are the angles of our boundary G(y 1 , y 2 ) = 0, which consists of lines y 1 = λ i (y 2 ) that form angles at intersection points, and these angles produce quadratic divergencies.…”

Section: Methods Of Proceeding In ε-Regularizationmentioning

confidence: 99%

Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II

Itoyama

Морозов²

2008

Progress of Theoretical Physics

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We further develop the formalism of arXiv:0712.0159 for the approximate solution of the Nambu-Goto (NG) equations with polygon conditions in AdS backgrounds, which is needed in modern studies of the string/gauge duality. The inscribed-circle condition is preserved, which leaves only one unknown function y 0 (y 1 , y 2 ) to solve and considerably simplifies our presentation. The problem is to find a delicate balance -if not an exact match -between two different structures: the NG equation (a nonlinear deformation of the Laplace equation with solutions nonlinearly deviating from holomorphic functions) and the boundary ring associated with polygons formed from null segments in Minkowski space. We provide more details about the theory of these structures and suggest an extended class of functions to be used at the next stage of the Alday-Maldacena program: the evaluation of regularized NG actions. §1. IntroductionIn this paper we begin our consideration of the next class of approximate solutions to the Nambu-Goto (NG) equations with null-polygon boundary conditions by the method suggested in 1). This problem is important for the study of the string/gauge (AdS/CFT) duality, 2), 3) reformulated recently 4)−28) as an identity between regularized minimal areas in AdS 5 and BDS/DHKS/BHT 7), 8), 17), 29) amplitudes for gluon scattering in N = 4 SUSY YM. Unfortunately, even after this groundbreaking reformulation, 4) no explicit check of duality has been carried out, even in the leading order of the strong-coupling expansion because of the usual technical difficulties on the string side. In this particular case, the first difficult problem is finding an explicit solution to a special version of the Plateau minimal-surface problem, 30) i.e., to the NG equations in AdS 5 geometry with the boundary conditions at the AdS boundary represented by a polygon Π with n lightlike (null) segments. We refer the readers to 4) for an explanation of how this polygon emerges in the problem after a sequence of transformations,and to 13) and 23) for additional comments and the notation. Irrespective of these motivations, the current formulation of the gauge/string duality is now purely geoDownloaded from https://academic.oup.

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New dual conformally invariant off-shell integrals

Cited by 35 publications

References 35 publications

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes

The massless supersymmetric ladder with L rungs

Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II

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