We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the -dimensional box integral with generic propagator powers is completely fixed by its symmetries to be a particular linear combination of Appell hypergeometric functions. In this context the Bloch-Wigner function arises as a special Yangian invariant in four dimensions. The bootstrap procedure for the box integral is naturally structured in algorithmic form. We then discuss the Yangian constraints for the six-point double box integral as well as for the related hexagon. For the latter we argue that the constraints are solved by a set of generalized Lauricella functions, and we comment on complications in identifying the integral as a certain linear combination of these. Finally, we elaborate on the close relation to the Mellin-Barnes technique and argue that it generates Yangian invariants as sums of residues.
{ "_oai": { "updated": "2021-08-29T04:58:27Z", "id": "oai:repo.scoap3.org:53239", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Florian Loebbert", "affiliations": [ { "country": "Germany", "value": "Institut f\u00fcr Physik, Humboldt-Universi\u00e4t zu Berlin, Zum Gro\u00dfen Windkanal 6, 12489 Berlin, Germany" } ], "surname": "Loebbert", "given_names": "Florian", "full_name": "Loebbert, Florian" }, { "raw_name": "Dennis M\u00fcller", "affiliations": [ { "country": "Denmark", "value": "Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark" } ], "surname": "M\u00fcller", "given_names": "Dennis", "full_name": "M\u00fcller, Dennis" }, { "raw_name": "Hagen M\u00fcnkler", "affiliations": [ { "country": "Switzerland", "value": "Institut f\u00fcr Theoretische Physik, Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich, Wolfgang-Pauli-Strasse 27, 8093 Z\u00fcrich, Switzerland" } ], "surname": "M\u00fcnkler", "given_names": "Hagen", "full_name": "M\u00fcnkler, Hagen" } ], "titles": [ { "source": "APS", "title": "Yangian bootstrap for conformal Feynman integrals" } ], "dois": [ { "value": "10.1103/PhysRevD.101.066006" } ], "publication_info": [ { "journal_volume": "101", "journal_title": "Physical Review D", "material": "article", "journal_issue": "6", "year": 2020 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-08-25T10:40:29.855947", "source": "APS", "method": "APS", "submission_number": "810b323c058f11ecb53772fd3742099d" }, "page_nr": [ 22 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2020" } ], "control_number": "53239", "record_creation_date": "2020-03-23T11:15:33.439049", "_files": [ { "checksum": "md5:8c35083ec1749711d05adcbc9e670dff", "filetype": "pdf", "bucket": "a300df12-1119-42aa-916b-6f76b7b59b16", "version_id": "bc439cee-dc85-4111-bd37-b1d4aaedd41c", "key": "10.1103/PhysRevD.101.066006.pdf", "size": 1383448 }, { "checksum": "md5:7ba69859c71fb72d244f6972d4ce9e34", "filetype": "xml", "bucket": "a300df12-1119-42aa-916b-6f76b7b59b16", "version_id": "d20863d9-9c88-439f-b01c-989902e98554", "key": "10.1103/PhysRevD.101.066006.xml", "size": 609772 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "hep-ph", "math-ph", "math.MP" ], "value": "1912.05561" } ], "abstracts": [ { "source": "APS", "value": "We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the <math><mi>D</mi></math>-dimensional box integral with generic propagator powers is completely fixed by its symmetries to be a particular linear combination of Appell hypergeometric functions. In this context the Bloch-Wigner function arises as a special Yangian invariant in four dimensions. The bootstrap procedure for the box integral is naturally structured in algorithmic form. We then discuss the Yangian constraints for the six-point double box integral as well as for the related hexagon. For the latter we argue that the constraints are solved by a set of generalized Lauricella functions, and we comment on complications in identifying the integral as a certain linear combination of these. Finally, we elaborate on the close relation to the Mellin-Barnes technique and argue that it generates Yangian invariants as sums of residues." } ], "imprints": [ { "date": "2020-03-11", "publisher": "APS" } ] }