Webs and Posets

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.

42 pages, 21 figures

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Cited by in corpus (19)

• Color-Kinematics Duality for QCD Amplitudes
• Bootstrapping the QCD soft anomalous dimension
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power
• From Webs to Polylogarithms
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Multiple Gluon Exchange Webs
• Multiparton webs beyond three loops
• An Introduction to Webs
• Cwebs beyond three loops in multiparton amplitudes
• Precise predictions for charged Higgs boson pair production in photon-photon collisions
• A factorization approach to next-to-leading-power threshold logarithms
• Local infrared safety in time-ordered perturbation theory
• Building blocks of Cwebs in multiparton scattering amplitudes
• Position-space cuts for Wilson line correlators
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• Path description of coordinate-space amplitudes
• Progress on soft gluon exponentiation and long-distance singularities
• Boomerang webs up to three-loop order