Gauge theory webs and surfaces

Erdoǧan, Ozan; Sterman, George

doi:10.1103/physrevd.91.016003

Cited by 25 publications

(61 citation statements)

References 80 publications

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“…It is then also necessary to develop techniques for carrying out the relevant Feynman integrals. Recently, there has been significant progress in this direction using configuration-space techniques both for strictly lightlike Wilson lines [37] and for non-lightlike lines [34,36,50,62]. The first three-loop results involving multiple Wilson lines have been published in ref.…”

Section: Jhep10(2014)010mentioning

confidence: 99%

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Multiple gluon exchange webs

Falcioni

Gardi

Harley

et al. 2014

J. High Energ. Phys.

120

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Webs are weighted sets of Feynman diagrams which build up the logarithms of correlators of Wilson lines, and provide the ingredients for the computation of the soft anomalous dimension. We present a general analysis of multiple gluon exchange webs (MGEWs) in correlators of semi-infinite non-lightlike Wilson lines, as functions of the exponentials of the Minkowski cusp angles, α ij , formed between lines i and j. We compute a range of webs in this class, connecting up to five Wilson lines through four loops, we give an all-loop result for a special class of diagrams, and we discover a new kind of relation between webs connecting different numbers of Wilson lines, based on taking collinear limits. Our results support recent conjectures, stating that the contribution of any MGEW to the soft anomalous dimension is a sum of products of polylogarithms, each depending on a single cusp angle, and such that their symbol alphabet is restricted to α ij and 1−α 2 ij . Finally, we construct a simple basis of functions, defined through a one-dimensional integral representation in terms of powers of logarithms, which has all the expected analytic properties. This basis allows us to compactly express the results of all MGEWs computed so far, and we conjecture that it is sufficient for expressing all MGEWs at any loop order.

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Section: Jhep10(2014)010mentioning

confidence: 99%

“…In N = 4 supersymmetric Yang-Mills theory, where much contemporary focus is on the planar limit, infrared singularities give access to non-planar effects (see, for example, refs. [28][29][30]), and they provide a link between the weak and strong coupling regimes [31][32][33][34][35][36][37][38][39].…”

Section: Jhep10(2014)010 1 Introductionmentioning

confidence: 99%

Multiple gluon exchange webs

Falcioni

Gardi

Harley

et al. 2014

J. High Energ. Phys.

120

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“…where Γ ∧ is this the anomalous dimension defined in eq. (1.8) with the geometry of Wilson lines shown in figure 3a and known to two loops [20]. Eq.…”

Section: Infrared Factorisation Of Form Factorsmentioning

confidence: 99%

Wilson-line geometries and the relation between IR singularities of form factors and the large-x limit of DGLAP splitting functions

Milloy¹,

Falcioni²,

Gardi³

2019

Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)

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We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimensions controlling single poles of these two quantities to all loops in terms of the closed parallelogram Wilson loop. To arrive at this result we first use the common hard-collinear behaviour of the two to derive a relation between their respective soft singularities, and then show that the latter is manifested in terms of differing Wilson-line geometries. We perform explicit diagrammatic calculations in configuration space through two loops to verify the relation. More generally, the emerging picture allows us to classify collinear singularities in eikonal quantities depending on whether they are associated with finite (closed) Wilson-line segments or infinite (open) ones.

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“…An important property of webs that can be proved in this way is that they lack soft or collinear subdivergences [8,15,16]. The webs of a given order automatically combine to cancel all divergences from singular regions where a proper subdiagram of a web is collinear to either one of the Wilson lines.…”

Section: (34)mentioning

confidence: 99%

“…Neglecting the running of α s , we find another analogy to minimal surfaces in five dimensions [16],…”

Section: Pos(radcor2015)027mentioning

confidence: 99%

A coordinate description of partonic processes

Sterman¹,

Erdoǧan²

2016

Proceedings of 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for

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We review a perturbative description of amplitudes in coordinate space, aiming at an intuitive perspective on the roles of "long" and "short" distances. We begin with coordinate-space leading regions for fixed-angle scattering amplitudes, and develop approximations and factorizations in analogy to similar procedures in momentum space. There are also applications to products of Wilson lines, including the familiar cusp amplitude. We briefly discuss cross sections from the coordinate viewpoint, and the mechanism by which infrared singularities cancel in inclusive cross sections.

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Gauge theory webs and surfaces

Abstract: We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances.

Cited by 25 publications

References 80 publications

Multiple gluon exchange webs

Multiple gluon exchange webs

Wilson-line geometries and the relation between IR singularities of form factors and the large-x limit of DGLAP splitting functions

A coordinate description of partonic processes

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