{"id":"https://openalex.org/W7214907763","doi":"https://doi.org/10.48550/arxiv.2609.36604","title":"Color Relations and Off-Shell Double-Copy for Towers of Theories","display_name":"Color Relations and Off-Shell Double-Copy for Towers of Theories","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214907763","doi":"https://doi.org/10.48550/arxiv.2609.36604"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36604","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36604","pdf_url":"https://arxiv.org/pdf/2609.36604","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/2609.36604","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153671302","display_name":"James Mangan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1354457","display_name":"Colorado Mesa University","ror":"https://ror.org/0451s5g67","country_code":"US","type":"education","lineage":["https://openalex.org/I1354457"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mangan, James","raw_affiliation_strings":["Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A","institution_ids":["https://openalex.org/I1354457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123466839","display_name":"Able Martinez","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1354457","display_name":"Colorado Mesa University","ror":"https://ror.org/0451s5g67","country_code":"US","type":"education","lineage":["https://openalex.org/I1354457"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martinez, Able","raw_affiliation_strings":["Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A","institution_ids":["https://openalex.org/I1354457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153579926","display_name":"Joseph Thomas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1354457","display_name":"Colorado Mesa University","ror":"https://ror.org/0451s5g67","country_code":"US","type":"education","lineage":["https://openalex.org/I1354457"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas, Joseph","raw_affiliation_strings":["Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical and Environmental Sciences , Colorado Mesa University , Grand Junction , Colorado 81521 , U.S.A","institution_ids":["https://openalex.org/I1354457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1354457"],"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9448000192642212,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9448000192642212,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.024399999529123306,"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":0.008299999870359898,"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/color-kinematics-duality","display_name":"color-kinematics duality","score":0.8790000081062317},{"id":"https://openalex.org/keywords/double-copy","display_name":"double copy","score":0.8029999732971191},{"id":"https://openalex.org/keywords/jacobi-identity","display_name":"Jacobi identity","score":0.9470000267028809},{"id":"https://openalex.org/keywords/soft-theorems","display_name":"soft theorems","score":0.8510000109672546},{"id":"https://openalex.org/keywords/on-shell-recursion-relations","display_name":"on-shell recursion relations","score":0.8080000281333923},{"id":"https://openalex.org/keywords/non-abelian-chern-simons-theory","display_name":"non-Abelian Chern-Simons theory","score":0.9599999785423279},{"id":"https://openalex.org/keywords/kinetic-mixing","display_name":"kinetic mixing","score":0.972000002861023},{"id":"https://openalex.org/keywords/gauge-conditions","display_name":"gauge conditions","score":0.4959999918937683}],"concepts":[{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.7426000237464905},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.7193999886512756},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5300999879837036},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.47600001096725464},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.39820000529289246},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3084000051021576},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36604","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36604","pdf_url":"https://arxiv.org/pdf/2609.36604","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.2609.36604","doi":"https://doi.org/10.48550/arxiv.2609.36604","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36604","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36604","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36604","pdf_url":"https://arxiv.org/pdf/2609.36604","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":[{"id":"https://openalex.org/F4320316016","display_name":"Colorado Mesa University","ror":"https://ror.org/0451s5g67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214907763.pdf","grobid_xml":"https://content.openalex.org/works/W7214907763.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1504165447","https://openalex.org/W1576586108","https://openalex.org/W1811565114","https://openalex.org/W2007148718","https://openalex.org/W2121190729","https://openalex.org/W2139470207","https://openalex.org/W2258126206","https://openalex.org/W4394644459"],"related_works":["https://openalex.org/W4289767410","https://openalex.org/W4417308929","https://openalex.org/W4385602960","https://openalex.org/W4309685528","https://openalex.org/W7211995561","https://openalex.org/W7021034462","https://openalex.org/W3045673906","https://openalex.org/W3191754568","https://openalex.org/W3191028542","https://openalex.org/W4309720289"],"abstract_inverted_index":{"Only":[0],"a":[1,61,93,100,114],"handful":[2],"of":[3,21,35,89,116],"elementary":[4],"color":[5],"building":[6],"blocks":[7],"are":[8,134],"known":[9],"to":[10,30],"participate":[11],"in":[12,72],"the":[13,18,27,32,48,90,126,159],"double":[14,28],"copy,":[15],"most":[16],"notably":[17],"structure":[19,54,128],"constants":[20],"gauge":[22,151],"theory.":[23],"This":[24],"work":[25],"extends":[26],"copy":[29],"include":[31],"infinite":[33],"family":[34],"totally":[36],"antisymmetric":[37],"``structure":[38],"constants''":[39],"with":[40,79,97],"arbitrarily":[41],"many":[42],"indices.":[43],"We":[44,111],"propose":[45],"and":[46,107,137],"motivate":[47],"Jacobi":[49],"identities":[50],"relating":[51],"these":[52],"$n$-index":[53,127],"constants.":[55,129],"For":[56],"each":[57,83],"$n$,":[58],"we":[59],"provide":[60,113],"derivatively-coupled":[62],"scalar":[63],"theory":[64,81],"that":[65,155,158],"is":[66,75,153,161],"color-dual":[67,162],"off-shell.":[68,163],"The":[69,130],"lowest":[70],"level":[71],"this":[73],"tower":[74,91,115,160],"two-dimensional":[76],"Zakharov-Mikhailov":[77],"theory,":[78],"one":[80],"for":[82],"higher":[84],"spacetime":[85],"dimension.":[86],"Each":[87],"member":[88],"exhibits":[92],"conserved":[94],"current":[95],"associated":[96],"color-kinematics":[98],"duality,":[99],"soft":[101],"theorem,":[102],"an":[103],"on-shell":[104],"recursion":[105],"relation,":[106],"classical":[108],"conformal":[109,139],"invariance.":[110],"also":[112],"modified":[117,131],"non-abelian":[118],"Chern-Simons":[119,132],"theories":[120,133],"whose":[121],"fields":[122],"couple":[123],"non-linearly":[124],"through":[125],"trivially":[135],"topological":[136],"classically":[138],"but":[140],"generally":[141],"exhibit":[142],"unusual":[143],"features":[144],"like":[145],"kinetic":[146],"mixing.":[147],"A":[148],"potentially":[149],"unphysical":[150],"condition":[152],"identified":[154],"would":[156],"ensure":[157]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
