Dukes, M., Gardi, E., McAslan, H., Scott, D.J. and White, C. (2014) Webs and posets. Journal of High Energy Physics, 2014(1), p. 24. (doi: 10.1007/JHEP01(2014)024)
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Publisher's URL: http://dx.doi.org/10.1007/JHEP01(2014)024
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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | McAslan, Miss Heather and White, Dr Christopher |
| Authors: | Dukes, M., Gardi, E., McAslan, H., Scott, D.J., and White, C. |
| College/School: | College of Science and Engineering > School of Physics and Astronomy |
| Journal Name: | Journal of High Energy Physics |
| Publisher: | Springer |
| ISSN: | 1029-8479 |
| Copyright Holders: | Copyright © 2014 The Authors |
| First Published: | First published in Journal of High Energy Physics 2014(1);24 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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