{"id":"https://openalex.org/W7223265899","doi":"https://doi.org/10.48550/arxiv.2610.30489","title":"Higher-Loop Vacuum Integrals on $S^D$","display_name":"Higher-Loop Vacuum Integrals on $S^D$","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223265899","doi":"https://doi.org/10.48550/arxiv.2610.30489"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30489","pdf_url":"https://arxiv.org/pdf/2610.30489","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.30489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016772566","display_name":"Varun Lochab","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lochab, Varun","raw_affiliation_strings":["Department of Physics , Columbia University , 538 West 120th Street , New York , New York 10027 , U.S"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Columbia University , 538 West 120th Street , New York , New York 10027 , U.S","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073714337","display_name":"Frederik Denef B","orcid":"https://orcid.org/0000-0003-4305-567X","observed_orcids":["https://orcid.org/0000-0003-4305-567X"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Denef, Frederik","raw_affiliation_strings":["Department of Physics , Columbia University , 538 West 120th Street , New York , New York 10027 , U.S"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Columbia University , 538 West 120th Street , New York , New York 10027 , U.S","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.4287000000476837,"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":0.4287000000476837,"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":0.31450000405311584,"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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.04149999842047691,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scalar-field-theory","display_name":"scalar field theory","score":0.7139999866485596},{"id":"https://openalex.org/keywords/sphere","display_name":"sphere","score":0.7509999871253967},{"id":"https://openalex.org/keywords/two-loop-feynman-diagrams","display_name":"two-loop Feynman diagrams","score":0.6980000138282776},{"id":"https://openalex.org/keywords/dimensional-regularization","display_name":"dimensional regularization","score":0.8270000219345093},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.3050000071525574}],"concepts":[{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5985999703407288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4952999949455261},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37720000743865967},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.3605000078678131},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33079999685287476},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.29589998722076416},{"id":"https://openalex.org/C65692021","wikidata":"https://www.wikidata.org/wiki/Q1094282","display_name":"Trigonometric integral","level":3,"score":0.29350000619888306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27889999747276306},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.27079999446868896},{"id":"https://openalex.org/C2992379347","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Feynman integral","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30489","pdf_url":"https://arxiv.org/pdf/2610.30489","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":"doi:10.48550/arxiv.2610.30489","doi":"https://doi.org/10.48550/arxiv.2610.30489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30489","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":"pmh:oai:arXiv.org:2610.30489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30489","pdf_url":"https://arxiv.org/pdf/2610.30489","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223265899.pdf","grobid_xml":"https://content.openalex.org/works/W7223265899.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4404987985"],"related_works":["https://openalex.org/W3098803475","https://openalex.org/W7103315216","https://openalex.org/W3040934413","https://openalex.org/W4404120777","https://openalex.org/W2726302145","https://openalex.org/W1968165255","https://openalex.org/W1979700438","https://openalex.org/W4255742584","https://openalex.org/W2339478282","https://openalex.org/W2524037315"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,16,34],"new":[3],"framework":[4],"for":[5,9,19,44,58,65],"evaluating":[6],"higher-loop":[7,21],"integrals":[8,22],"scalar":[10],"fields":[11],"on":[12,23],"$S^D$.":[13],"Starting":[14],"from":[15],"Schwinger-parametric":[17],"form":[18],"general":[20,66],"the":[24,55,62],"sphere,":[25],"it":[26],"combines":[27],"total-derivative":[28],"identities":[29],"with":[30],"edge-contraction":[31],"relations":[32],"into":[33],"coupled":[35],"linear":[36],"system.":[37],"To":[38],"illustrate":[39],"our":[40],"method,":[41],"we":[42,60],"solve":[43],"all":[45,75],"vacuum":[46],"graphs":[47],"through":[48],"two":[49],"loops.":[50],"This":[51],"includes,":[52],"in":[53],"particular,":[54],"two-loop":[56],"three-melon,":[57],"which":[59],"construct":[61],"analytic":[63],"solution":[64],"$D$":[67],"and":[68],"obtain":[69],"explicit":[70],"dimensionally":[71],"regularized":[72],"results":[73],"at":[74],"integer":[76],"dimensions.":[77]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}
