{"id":"https://openalex.org/W7220690073","doi":"https://doi.org/10.48550/arxiv.2610.03864","title":"Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders","display_name":"Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220690073","doi":"https://doi.org/10.48550/arxiv.2610.03864"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03864","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03864","pdf_url":"https://arxiv.org/pdf/2610.03864","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/2610.03864","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157701852","display_name":"Ryohei Kobayashi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kobayashi, Ryohei","raw_affiliation_strings":["Department of Applied Physics , University of Tokyo , Bunkyo-ku , Tokyo 113-8656 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics , University of Tokyo , Bunkyo-ku , Tokyo 113-8656 , Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067061486","display_name":"Abhinav Prem","orcid":"https://orcid.org/0000-0003-4438-7107","observed_orcids":["https://orcid.org/0000-0003-4438-7107"]},"institutions":[{"id":"https://openalex.org/I39661318","display_name":"Bard College","ror":"https://ror.org/04yrgt058","country_code":"US","type":"education","lineage":["https://openalex.org/I39661318"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prem, Abhinav","raw_affiliation_strings":["Physics Program , Bard College , 30 Campus Road , Annandale-on-Hudson , New York 12504 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Program , Bard College , 30 Campus Road , Annandale-on-Hudson , New York 12504 , USA","institution_ids":["https://openalex.org/I39661318"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157693360","display_name":"Matthew Yu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu, Matthew","raw_affiliation_strings":["School of Natural Sciences , Institute for Advanced Study , 1 Einstein Drive , Princeton , NJ 08540 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Natural Sciences , Institute for Advanced Study , 1 Einstein Drive , Princeton , NJ 08540 , USA","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.3617999851703644,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10657","display_name":"Topological Materials and Phenomena","score":0.3617999851703644,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11804","display_name":"Quantum many-body systems","score":0.2320999950170517,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.17810000479221344,"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/higher-form-symmetries","display_name":"higher-form symmetries","score":0.9070000052452087},{"id":"https://openalex.org/keywords/gravity-anomalies","display_name":"gravity anomalies","score":0.5199999809265137},{"id":"https://openalex.org/keywords/emergent-fermions","display_name":"emergent fermions","score":0.7839999794960022},{"id":"https://openalex.org/keywords/line-operators","display_name":"line operators","score":0.8410000205039978},{"id":"https://openalex.org/keywords/gauging","display_name":"gauging","score":0.777999997138977},{"id":"https://openalex.org/keywords/decoherence","display_name":"decoherence","score":0.8460000157356262},{"id":"https://openalex.org/keywords/topological-operators","display_name":"topological operators","score":0.8569999933242798},{"id":"https://openalex.org/keywords/lattice-model","display_name":"lattice model","score":0.6980000138282776}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6805999875068665},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.5544000267982483},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5507000088691711},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4832000136375427},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4415000081062317},{"id":"https://openalex.org/C2778971668","wikidata":"https://www.wikidata.org/wiki/Q5510284","display_name":"Fusion rules","level":4,"score":0.4374000132083893},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.41769999265670776},{"id":"https://openalex.org/C92542899","wikidata":"https://www.wikidata.org/wiki/Q7661340","display_name":"Symmetry protected topological order","level":4,"score":0.4092999994754791},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3926999866962433},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C45646460","wikidata":"https://www.wikidata.org/wiki/Q17165159","display_name":"Topological order","level":3,"score":0.35989999771118164},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30630001425743103},{"id":"https://openalex.org/C199793620","wikidata":"https://www.wikidata.org/wiki/Q7825030","display_name":"Topological degeneracy","level":5,"score":0.2948000133037567},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C7503960","wikidata":"https://www.wikidata.org/wiki/Q721094","display_name":"Topological quantum field theory","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C104862878","wikidata":"https://www.wikidata.org/wiki/Q1770567","display_name":"Topological defect","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03864","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03864","pdf_url":"https://arxiv.org/pdf/2610.03864","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.2610.03864","doi":"https://doi.org/10.48550/arxiv.2610.03864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03864","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:2610.03864","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03864","pdf_url":"https://arxiv.org/pdf/2610.03864","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/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220690073.pdf","grobid_xml":"https://content.openalex.org/works/W7220690073.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1975614225","https://openalex.org/W2170604368","https://openalex.org/W2907352505","https://openalex.org/W2945426239","https://openalex.org/W3035520321","https://openalex.org/W3093467580","https://openalex.org/W3169644112","https://openalex.org/W4297370039","https://openalex.org/W4300972269","https://openalex.org/W4307936367","https://openalex.org/W4316843755","https://openalex.org/W4319453772","https://openalex.org/W4360612392","https://openalex.org/W4367854170","https://openalex.org/W4392781398","https://openalex.org/W4393299255","https://openalex.org/W4402500712","https://openalex.org/W4402701028","https://openalex.org/W4402927405","https://openalex.org/W4403498531","https://openalex.org/W4404390801","https://openalex.org/W4405904183","https://openalex.org/W4406661666","https://openalex.org/W4407762076","https://openalex.org/W4408334597","https://openalex.org/W4410383279","https://openalex.org/W4411931815","https://openalex.org/W4413657806","https://openalex.org/W4414508160","https://openalex.org/W4414812757","https://openalex.org/W4415315143","https://openalex.org/W4416017109","https://openalex.org/W4416053403","https://openalex.org/W4416059809","https://openalex.org/W4416101625","https://openalex.org/W4416258749","https://openalex.org/W4416517636","https://openalex.org/W4417266641","https://openalex.org/W4417268315","https://openalex.org/W6910709126","https://openalex.org/W6929051431","https://openalex.org/W6929452573","https://openalex.org/W6948226624","https://openalex.org/W7102555488","https://openalex.org/W7164415703","https://openalex.org/W7165355571","https://openalex.org/W7166181867","https://openalex.org/W7166640191"],"related_works":["https://openalex.org/W1892605745","https://openalex.org/W3108943770","https://openalex.org/W4416258749","https://openalex.org/W7124442274","https://openalex.org/W3086534197","https://openalex.org/W1725378648","https://openalex.org/W6948188489","https://openalex.org/W4415357517","https://openalex.org/W4406662082","https://openalex.org/W4280602024"],"abstract_inverted_index":{"We":[0,15,40,85],"construct":[1],"large":[2],"families":[3],"of":[4,57,78,112,115,129],"mixed-state":[5,12,37,122,158],"topological":[6,13,38,113,123,161],"orders":[7,124],"in":[8,54,138],"(3+1)D,":[9],"including":[10],"intrinsically":[11,121,157],"orders.":[14],"realize":[16],"these":[17],"theories":[18,48],"by":[19,104,126],"relating":[20],"the":[21,28,55,66,76,110,127],"data":[22,77,89],"parameterizing":[23],"braided":[24,79,94],"fusion":[25,80,95],"2-categories":[26,81],"to":[27],"strong":[29,105,130],"higher-form":[30,131],"symmetries":[31,132],"and":[32,73,90,106],"their":[33],"anomalies":[34,134],"that":[35,92,147],"characterize":[36],"order.":[39],"focus":[41],"here":[42],"on":[43,65],"bosonic":[44],"theories,":[45],"which":[46,49,166],"include":[47],"admit":[50],"an":[51],"emergent":[52],"fermion":[53],"spectrum":[56],"line":[58],"operators.":[59],"Our":[60],"general":[61,100],"framework":[62],"is":[63],"exemplified":[64],"lattice,":[67],"where":[68],"we":[69,145],"present":[70],"concrete":[71],"models":[72],"identify":[74],"how":[75],"are":[82],"physically":[83],"encoded.":[84],"then":[86],"formalize":[87],"this":[88],"show":[91,146],"every":[93],"2-category":[96],"arises":[97],"from":[98],"a":[99,116,150,168],"construction":[101],"(decoherence":[102],"followed":[103],"weak":[107],"gauging)":[108],"as":[109],"category":[111],"operators":[114,162],"(3+1)D":[117,140,148],"mixed":[118],"state,":[119],"with":[120,153],"distinguished":[125],"presence":[128],"whose":[133,160],"cannot":[135],"be":[136],"realized":[137],"any":[139],"gapped":[141],"ground":[142],"state.":[143],"Notably,":[144],"admits":[149],"new":[151],"mechanism":[152],"no":[154],"(2+1)D":[155],"counterpart:":[156],"order":[159],"braid":[163],"non-degenerately,":[164],"but":[165],"carries":[167],"gravitational":[169],"anomaly.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-07T00:00:00"}