{"id":"https://openalex.org/W4226310470","doi":"https://doi.org/10.1007/jhep06(2026)067","title":"Kinematics, cluster algebras and Feynman integrals","display_name":"Kinematics, cluster algebras and Feynman integrals","publication_year":2026,"publication_date":"2026-06-05","ids":{"openalex":"https://openalex.org/W4226310470","doi":"https://doi.org/10.1007/jhep06(2026)067"},"language":"en","primary_location":{"id":"doi:10.1007/jhep06(2026)067","doi":"https://doi.org/10.1007/jhep06(2026)067","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2026)067","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2026)067.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2026)067.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023543729","display_name":"Song Lin He","orcid":"https://orcid.org/0000-0002-9534-3844","observed_orcids":["https://orcid.org/0000-0002-9534-3844","https://orcid.org/0000-0002-2702-8914"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210101410","display_name":"International Centre for Theoretical Physics Asia-Pacific","ror":"https://ror.org/01z2px678","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210101410","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I4210112519","display_name":"Peng Huanwu Center for Fundamental Theory","ror":"https://ror.org/01s9dmg43","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112519"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song He","raw_affiliation_strings":["Chinese Academy of Sciences","ICTP-AP International Centre for Theoretical Physics Asia-Pacific","Peng Huanwu Center for Fundamental Theory","UCAS","University of Chinese Academy of Sciences"],"raw_orcid":"https://orcid.org/0000-0002-9534-3844","affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"ICTP-AP International Centre for Theoretical Physics Asia-Pacific","institution_ids":["https://openalex.org/I4210101410"]},{"raw_affiliation_string":"Peng Huanwu Center for Fundamental Theory","institution_ids":["https://openalex.org/I4210112519"]},{"raw_affiliation_string":"UCAS","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100764339","display_name":"Zhenjie Li","orcid":"https://orcid.org/0000-0001-7111-9402","observed_orcids":["https://orcid.org/0000-0001-7111-9402"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenjie Li","raw_affiliation_strings":["Chinese Academy of Sciences","University of Chinese Academy of Sciences"],"raw_orcid":"https://orcid.org/0000-0001-7111-9402","affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071062179","display_name":"Qinglin Yang","orcid":"https://orcid.org/0000-0002-7263-8914","observed_orcids":["https://orcid.org/0000-0002-7263-8914","https://orcid.org/0000-0002-1964-0935"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qinglin Yang","raw_affiliation_strings":["Chinese Academy of Sciences","University of Chinese Academy of Sciences"],"raw_orcid":"https://orcid.org/0000-0002-1964-0935","affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071062179"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":7.5407,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9691852,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"2026","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.3774000108242035,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.3774000108242035,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.28130000829696655,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.14059999585151672,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-algebras","display_name":"cluster algebras","score":0.9760000109672546},{"id":"https://openalex.org/keywords/planar-kinematics","display_name":"planar kinematics","score":0.7910000085830688},{"id":"https://openalex.org/keywords/cluster-variables","display_name":"cluster variables","score":0.9409999847412109},{"id":"https://openalex.org/keywords/dimensional-reduction","display_name":"dimensional reduction","score":0.8389999866485596},{"id":"https://openalex.org/keywords/three-loop-integrals","display_name":"three-loop integrals","score":0.6809999942779541},{"id":"https://openalex.org/keywords/differential-equations","display_name":"differential equations","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C65574998","wikidata":"https://www.wikidata.org/wiki/Q386272","display_name":"Feynman diagram","level":2,"score":0.7103351950645447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5614036321640015},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5159679055213928},{"id":"https://openalex.org/C54937798","wikidata":"https://www.wikidata.org/wiki/Q2024141","display_name":"Massless particle","level":2,"score":0.449954092502594},{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.44704392552375793},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4204566776752472},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.418376624584198},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32315248250961304},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2754739224910736},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.24654927849769592},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20932236313819885},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16352564096450806},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/jhep06(2026)067","doi":"https://doi.org/10.1007/jhep06(2026)067","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2026)067","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2026)067.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2112.11842","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2112.11842","pdf_url":"https://arxiv.org/pdf/2112.11842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:5d5e51d34f2d4f51ad318580cf6c980c","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/5d5e51d34f2d4f51ad318580cf6c980c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of High Energy Physics, Vol 2026, Iss 6 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2112.11842","doi":"https://doi.org/10.48550/arxiv.2112.11842","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2112.11842","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/jhep06(2026)067","doi":"https://doi.org/10.1007/jhep06(2026)067","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2026)067","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2026)067.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4702203532","display_name":"\u6563\u5c04\u632f\u5e45\u7684\u65b0\u7406\u8bba\u3001\u65b0\u65b9\u6cd5\u53ca\u5176\u5e94\u7528","funder_award_id":"11935013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7654887179","display_name":null,"funder_award_id":"12047502","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8181039722","display_name":null,"funder_award_id":"12047503","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8887143334","display_name":null,"funder_award_id":"11947301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226310470.pdf","grobid_xml":"https://content.openalex.org/works/W4226310470.grobid-xml"},"referenced_works_count":82,"referenced_works":["https://openalex.org/W1898987871","https://openalex.org/W1968838851","https://openalex.org/W1970198451","https://openalex.org/W1973074703","https://openalex.org/W1983525968","https://openalex.org/W1984797944","https://openalex.org/W1988596207","https://openalex.org/W1996717373","https://openalex.org/W2016530342","https://openalex.org/W2029679650","https://openalex.org/W2030826336","https://openalex.org/W2032556563","https://openalex.org/W2041848171","https://openalex.org/W2045038970","https://openalex.org/W2058502187","https://openalex.org/W2064312985","https://openalex.org/W2068283118","https://openalex.org/W2076583843","https://openalex.org/W2079988604","https://openalex.org/W2094419403","https://openalex.org/W2103836394","https://openalex.org/W2117726506","https://openalex.org/W2131654852","https://openalex.org/W2133548243","https://openalex.org/W2135900651","https://openalex.org/W2139743966","https://openalex.org/W2155737582","https://openalex.org/W2160038359","https://openalex.org/W2164406307","https://openalex.org/W2258126206","https://openalex.org/W2514839738","https://openalex.org/W2564790176","https://openalex.org/W2613533455","https://openalex.org/W2766001861","https://openalex.org/W2788033499","https://openalex.org/W2804276131","https://openalex.org/W2806832732","https://openalex.org/W2808582071","https://openalex.org/W2896020678","https://openalex.org/W2904764405","https://openalex.org/W2924028028","https://openalex.org/W2949725221","https://openalex.org/W2954838498","https://openalex.org/W2964007711","https://openalex.org/W2972638409","https://openalex.org/W2972665428","https://openalex.org/W2977294739","https://openalex.org/W2984193198","https://openalex.org/W2994956345","https://openalex.org/W2995739357","https://openalex.org/W2996680249","https://openalex.org/W3023565342","https://openalex.org/W3037609493","https://openalex.org/W3038941373","https://openalex.org/W3040029887","https://openalex.org/W3044611482","https://openalex.org/W3068532603","https://openalex.org/W3088760370","https://openalex.org/W3105262559","https://openalex.org/W3113935014","https://openalex.org/W3115916304","https://openalex.org/W3116993492","https://openalex.org/W3117989501","https://openalex.org/W3135286957","https://openalex.org/W3135522479","https://openalex.org/W3135635141","https://openalex.org/W3159172364","https://openalex.org/W3166661921","https://openalex.org/W3166740469","https://openalex.org/W3166865471","https://openalex.org/W3167097351","https://openalex.org/W3170496325","https://openalex.org/W3171830449","https://openalex.org/W3174156932","https://openalex.org/W3175202201","https://openalex.org/W3194608885","https://openalex.org/W4200109199","https://openalex.org/W4220725620","https://openalex.org/W4280524328","https://openalex.org/W4285674539","https://openalex.org/W4394640777","https://openalex.org/W6929960052"],"related_works":["https://openalex.org/W3166661921","https://openalex.org/W3135635141","https://openalex.org/W3135522479","https://openalex.org/W4320351970","https://openalex.org/W4391477269","https://openalex.org/W4293196246","https://openalex.org/W7135033736","https://openalex.org/W6969114059","https://openalex.org/W2808582071","https://openalex.org/W4407064480"],"abstract_inverted_index":{"A":[0],"bstract":[1],"We":[2,33,77],"identify":[3],"cluster":[4,19,55,90,129,168],"algebras":[5,20,36,91],"for":[6,21,37,71,149],"planar":[7],"kinematics":[8,112],"of":[9,18,47,73,94],"conformal":[10],"Feynman":[11,50,75,95],"integrals":[12,51,96],"in":[13,97,117,121,142],"four":[14],"dimensions,":[15],"as":[16],"sub-algebras":[17],"Grassmannian":[22],"G":[23],"(4,":[24],"n":[25,29],")":[26],"corresponding":[27,49],"to":[28,65,114,123,163],"-point":[30],"massless":[31],"kinematics.":[32],"classify":[34],"such":[35],"cases":[38],"through":[39],"eight":[40],"points,":[41],"and":[42,57,87],"provide":[43],"evidence":[44],"that":[45,80,127],"singularities":[46,93],"the":[48,88,118],"are":[52,128],"given":[53],"by":[54,85,167],"variables":[56],"their":[58],"algebraic":[59,135],"generalizations.":[60],"By":[61],"sending":[62],"a":[63,101,106,138],"point":[64],"infinity,":[66],"our":[67],"results":[68,145],"have":[69],"implications":[70],"symbology":[72],"non-conformal":[74,119],"integrals.":[76],"also":[78,132],"find":[79,133],"dimensional":[81],"reduction":[82],"is":[83],"achieved":[84],"folding":[86],"resulting":[89],"encode":[92],"three":[98,134],"dimensions.":[99],"As":[100],"highly-nontrivial":[102],"application,":[103],"we":[104,131,156],"study":[105],"eight-point":[107],"three-loop":[108],"wheel":[109],"integral":[110],"whose":[111],"correspond":[113],"two-mass-easy":[115],"box":[116],"limit:":[120],"addition":[122],"nine":[124],"rational":[125],"letters":[126,136],"variables,":[130],"containing":[137],"new":[139],"square":[140],"root,":[141],"accordance":[143],"with":[144],"from":[146],"differential":[147],"equations":[148],"two-loop":[150],"case.":[151],"Based":[152],"on":[153],"this":[154],"alphabet,":[155],"bootstrap":[157],"its":[158],"symbol,":[159],"which":[160],"turns":[161],"out":[162],"be":[164],"strongly":[165],"constrained":[166],"adjacency":[169],"conditions.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2022-05-05T00:00:00"}