Webs and posets

Mark Dukes, Einan Gardi, Heather McAslan, Darren Scott, Chris D. White

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together give rise to colour factors corresponding to connected graphs. The colour and kinematic degrees of freedom of individual diagrams in a web are entangled by mixing matrices of purely combinatorial origin. In this paper we relate the combinatorial study of these matrices to properties of partially ordered sets (posets), and hence obtain explicit solutions for certain families of web-mixing matrix, at arbitrary order in perturbation theory. We also provide a general expression for the rank of a general class of mixing matrices, which governs the number of independent colour factors arising from such webs. Finally, we use the poset language to examine a previously conjectured sum rule for the columns of web-mixing matrices which governs the cancellation of the leading subdivergences between diagrams in the web. Our results, when combined with parallel developments in the evaluation of kinematic integrals, offer new insights into the all-order structure of infrared singularities in non-Abelian gauge theories.
LanguageEnglish
Article number24
Number of pages43
JournalJournal of High Energy Physics
Volume2014
Issue number1
DOIs
Publication statusPublished - 8 Jan 2014

Fingerprint

matrices
diagrams
correlators
color
kinematics
cancellation
sum rules
gauge theory
theorems
perturbation theory
degrees of freedom
operators
expansion
evaluation

Keywords

  • scattering amplitudes
  • resummation
  • non-Abelian exponentiation theorem

Cite this

Dukes, M., Gardi, E., McAslan, H., Scott, D., & White, C. D. (2014). Webs and posets. Journal of High Energy Physics, 2014(1), [24]. https://doi.org/10.1007/JHEP01(2014)024
Dukes, Mark ; Gardi, Einan ; McAslan, Heather ; Scott, Darren ; White, Chris D. / Webs and posets. In: Journal of High Energy Physics. 2014 ; Vol. 2014, No. 1.
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Dukes, M, Gardi, E, McAslan, H, Scott, D & White, CD 2014, 'Webs and posets' Journal of High Energy Physics, vol. 2014, no. 1, 24. https://doi.org/10.1007/JHEP01(2014)024

Webs and posets. / Dukes, Mark; Gardi, Einan; McAslan, Heather; Scott, Darren; White, Chris D.

In: Journal of High Energy Physics, Vol. 2014, No. 1, 24, 08.01.2014.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Webs and posets

AU - Dukes, Mark

AU - Gardi, Einan

AU - McAslan, Heather

AU - Scott, Darren

AU - White, Chris D.

PY - 2014/1/8

Y1 - 2014/1/8

N2 - The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together give rise to colour factors corresponding to connected graphs. The colour and kinematic degrees of freedom of individual diagrams in a web are entangled by mixing matrices of purely combinatorial origin. In this paper we relate the combinatorial study of these matrices to properties of partially ordered sets (posets), and hence obtain explicit solutions for certain families of web-mixing matrix, at arbitrary order in perturbation theory. We also provide a general expression for the rank of a general class of mixing matrices, which governs the number of independent colour factors arising from such webs. Finally, we use the poset language to examine a previously conjectured sum rule for the columns of web-mixing matrices which governs the cancellation of the leading subdivergences between diagrams in the web. Our results, when combined with parallel developments in the evaluation of kinematic integrals, offer new insights into the all-order structure of infrared singularities in non-Abelian gauge theories.

AB - The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together give rise to colour factors corresponding to connected graphs. The colour and kinematic degrees of freedom of individual diagrams in a web are entangled by mixing matrices of purely combinatorial origin. In this paper we relate the combinatorial study of these matrices to properties of partially ordered sets (posets), and hence obtain explicit solutions for certain families of web-mixing matrix, at arbitrary order in perturbation theory. We also provide a general expression for the rank of a general class of mixing matrices, which governs the number of independent colour factors arising from such webs. Finally, we use the poset language to examine a previously conjectured sum rule for the columns of web-mixing matrices which governs the cancellation of the leading subdivergences between diagrams in the web. Our results, when combined with parallel developments in the evaluation of kinematic integrals, offer new insights into the all-order structure of infrared singularities in non-Abelian gauge theories.

KW - scattering amplitudes

KW - resummation

KW - non-Abelian exponentiation theorem

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Dukes M, Gardi E, McAslan H, Scott D, White CD. Webs and posets. Journal of High Energy Physics. 2014 Jan 8;2014(1). 24. https://doi.org/10.1007/JHEP01(2014)024