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The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respectively to differential forms defining master integrals, and integration contours which place a subset of the propagators on shell. In a canonical basis these forms and contours are dual to each other. In this talk I review our present understanding of this algebraic structure and its manifestation for dimensionally-regularized Feynman integrals that are expandable to polylogarithms around integer dimensions. Using one- and two-loop integral examples, I will explain the duality between forms and contours, and the correspondence between the local coaction acting on the Laurent coefficients in the dimensional regulator and the global coaction acting on generalised hypergeometric functions. The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respectively to differential forms defining master integrals, and integration contours which place a subset of the propagators on shell. In a canonical basis these forms and contours are dual to each other. In this talk I review our present understanding of this algebraic structure and its manifestation for dimensionally-regularized Feynman integrals that are expandable to polylogarithms around integer dimensions. Using one- and two-loop integral examples, I will explain the duality between forms and contours, and the correspondence between the local coaction acting on the Laurent coefficients in the dimensional regulator and the global coaction acting on generalised hypergeometric functions. 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var affiliation = $(this).data('affiliation') + '</br>'; var contribution = $(this).data('contribution') + '</br>'; $.magnificPopup.open({ items: { src: '<div id="ovelary-mathjax" class="overlay-white oc-content overlay-white-500">' + author + affiliation + contribution + '</div>', type: 'inline' }, callbacks: { open: function() { var div = document.getElementById("overlay-mathjax") MathJax.Hub.Queue(["Typeset", MathJax.Hub, div]); }, } }) }) }); </script> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;"><a href="http://arxiv.org/abs/arXiv:2207.07843">arXiv:2207.07843</a> ; CERN-TH-2022-122 ; BONN-TH-2022-18</td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>The Diagrammatic Coaction</b></td></tr> <tr><td class="formatRecordLabel"><span style="white-space:nowrap;"> Author(s) </span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Gardi%2C%20Einan&ln=en">Gardi, Einan</a> (Edinburgh U.) ; <a href="https://cds.cern.ch/search?f=author&p=Abreu%2C%20Samuel&ln=en">Abreu, Samuel</a> (CERN ; Edinburgh U.) ; <a href="https://cds.cern.ch/search?f=author&p=Britto%2C%20Ruth&ln=en">Britto, Ruth</a> (Trinity Coll., Dublin) ; <a href="https://cds.cern.ch/search?f=author&p=Duhr%2C%20Claude&ln=en">Duhr, Claude</a> (Bonn U.) ; <a href="https://cds.cern.ch/search?f=author&p=Matthew%2C%20James&ln=en">Matthew, James</a> (Edinburgh U.)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">2022-10-20</td></tr> <tr><td class="formatRecordLabel"> Imprint </td><td style="padding-left:5px;">2022-07-16</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">19</td></tr> <tr><td class="formatRecordLabel"> Note </td><td style="padding-left:5px;">19 pages, Talk presented at Loop and Legs in Quantum Field Theory - LL2022, 25-30 April, 2022, Ettal, Germany</td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.416.0015"><i>PoS</i> LL2022 (2022) 015</a> </a></td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/record/2824159">16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022</a>, Ettal, Germany, 25 - 30 Apr 2022, pp.015</td></tr> <tr><td class="formatRecordLabel"> DOI </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.416.0015" title="DOI" target="_blank">10.22323/1.416.0015</a> <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">Particle Physics - Phenomenology ; Particle Physics - Theory</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respectively to differential forms defining master integrals, and integration contours which place a subset of the propagators on shell. In a canonical basis these forms and contours are dual to each other. In this talk I review our present understanding of this algebraic structure and its manifestation for dimensionally-regularized Feynman integrals that are expandable to polylogarithms around integer dimensions. Using one- and two-loop integral examples, I will explain the duality between forms and contours, and the correspondence between the local coaction acting on the Laurent coefficients in the dimensional regulator and the global coaction acting on generalised hypergeometric functions.</td></tr> <tr><td class="formatRecordLabel"> Copyright/License </td><td style="padding-left:5px;">publication: © 2022-2024 The authors (License: <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/">CC-BY-NC-ND-4.0</a>)<br/>preprint: (License: <a href="http://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>)</td></tr> </table> <br /><div style="max-width:1024px;margin:auto"><div style="overflow-x:auto;display:inline;width:100%;"><a href="/record/2816198/plots#0"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2816198/files/triPRL.png" title=" \cal O1-\zzp_1^21-\zbar" width="200px"/></a> <a href="/record/2816198/plots#1"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2816198/files/bub12PRL.png" title=" \cal O1-\zzp_1^21-\zbar" width="200px"/></a> <a href="/record/2816198/plots#2"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2816198/files/bub13PRL.png" title=" \cal O1-\zzp_1^21-\zbar" width="200px"/></a> <a href='/record/2816198/plots'>Show more plots</a></div></div><br /> <br/>Corresponding record in: <a href="http://inspirehep.net/record/2116101">Inspire</a> <small> </small> <br/> <br/><br/><div align="right"><div style="padding-bottom:2px;padding-top:30px;"><span class="moreinfo" style="margin-right:10px;"> <a href="" class="moreinfo">Back to search</a> </span></div></div> <div class="bottom-left-folded"><div class="recordlastmodifiedbox" style="position:relative;margin-left:1px"> Record created 2022-07-20, last modified 2023-08-29</div></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=en&p=recid%3A2816198&rm=wrd" class="moreinfo">Similar records</a></span></div> </div> </div> </div> <br/> <br /> <div class="detailedrecordminipanel"> <div class="top-left"></div><div class="top-right"></div> <div class="inside"> <div id="detailedrecordminipanelfile" style="width:33%;float:left;text-align:center;margin-top:0"> <div><small class="detailedRecordActions">Fulltext:</small> <br /><em>document</em> - <a href="/record/2816198/files/document.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Download fulltext"/>PDF</a><br /><em>2207.07843</em> - <a href="/record/2816198/files/2207.07843.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Download fulltext"/>PDF</a><br /></div> </div> <div id="detailedrecordminipanelreview" style="width:30%;float:left;text-align:center"> </div> <div id="detailedrecordminipanelactions" style="width:36%;float:right;text-align:right;"> <ul class="detailedrecordactions"> <li><a href="/yourbaskets/add?ln=en&recid=2816198">Add to personal basket</a></li> <li>Export as <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/hx?ln=en">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/hm?ln=en">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/xm?ln=en">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/xd?ln=en">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/xe?ln=en">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/xn?ln=en">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2816198/export/xw?ln=en">RefWorks</a> </li> </ul> <div style='padding-left: 13px;'>  <div id="bookmark"></div> <div id="bookmark_sciencewise"></div> <style type="text/css"> #bookmark_sciencewise, #bookmark {float: left;} #bookmark_sciencewise li {padding: 2px; width: 25px;} #bookmark_sciencewise ul, #bookmark ul {list-style-image: none;} </style> <script type="text/javascript" src="/js/jquery.bookmark.min.js"></script> <style type="text/css">@import "/css/jquery.bookmark.css";</style> <script type="text/javascript">// <![CDATA[ $.bookmark.addSite('sciencewise', 'ScienceWise.info', 'https://cds.cern.ch/img/sciencewise.png', 'en', 'bookmark', 'http://sciencewise.info/bookmarks/2207.0784/add'); $('#bookmark_sciencewise').bookmark({sites: ['sciencewise']}); $('#bookmark').bookmark({ sites: ['facebook', 'twitter', 'linkedin', 'google_plusone'], icons: '/img/bookmarks.png', url: 'https://cds.cern.ch/record/2816198', addEmail: true, title: "The Diagrammatic Coaction", description: "The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. 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