Webs and posets

doi:10.1007/JHEP01(2014)024

Webs and posets

2014-01-08

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DOI：10.1007/JHEP01(2014)024

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The non-Abelian exponentiation theorem has recently been generalised to cor- relators 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 fac- tors corresponding to connected graphs. The colour and kinematic degrees of freedom of in- dividual 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.

Keywords:

QCD

Scattering Amplitudes

Resummation

Webs and posets

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