Abstract
| Language | English |
|---|---|
| Article number | 24 |
| Number of pages | 43 |
| Journal | Journal of High Energy Physics |
| Volume | 2014 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 8 Jan 2014 |
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Keywords
- scattering amplitudes
- resummation
- non-Abelian exponentiation theorem
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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 journal › Article
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
UR - http://arxiv.org/abs/1310.3127
U2 - 10.1007/JHEP01(2014)024
DO - 10.1007/JHEP01(2014)024
M3 - Article
VL - 2014
JO - Journal of High Energy Physics
T2 - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1029-8479
IS - 1
M1 - 24
ER -