{"id":"https://openalex.org/W7223068643","doi":"https://doi.org/10.48550/arxiv.2610.26610","title":"The $A_3$ Narain family over $\\mathbb{Z}_4$","display_name":"The $A_3$ Narain family over $\\mathbb{Z}_4$","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223068643","doi":"https://doi.org/10.48550/arxiv.2610.26610"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26610","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26610","pdf_url":"https://arxiv.org/pdf/2610.26610","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/2610.26610","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009478916","display_name":"R. Sammani","orcid":"https://orcid.org/0009-0001-8575-4025","observed_orcids":["https://orcid.org/0009-0001-8575-4025"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sammani, Rajae","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088537530","display_name":"Abdellah Sebbar","orcid":"https://orcid.org/0000-0002-1433-8016","observed_orcids":["https://orcid.org/0000-0002-1433-8016"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sebbar, Abdellah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9042999744415283,"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":0.9042999744415283,"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":0.05790000036358833,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.012000000104308128,"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/z4-codes","display_name":"Z4 codes","score":0.8270000219345093},{"id":"https://openalex.org/keywords/construction-a","display_name":"Construction A","score":0.777999997138977},{"id":"https://openalex.org/keywords/t-duality","display_name":"T-duality","score":0.7950000166893005},{"id":"https://openalex.org/keywords/magnetic-flux-density","display_name":"magnetic flux density","score":0.5230000019073486},{"id":"https://openalex.org/keywords/theta-series","display_name":"theta series","score":0.8539999723434448},{"id":"https://openalex.org/keywords/self-dual-codes","display_name":"self-dual codes","score":0.7799999713897705},{"id":"https://openalex.org/keywords/twisted-sectors","display_name":"twisted sectors","score":0.5189999938011169}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6525999903678894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6184999942779541},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5825999975204468},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.5356000065803528},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.491100013256073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4814999997615814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39989998936653137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3684000074863434},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3237000107765198},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26610","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26610","pdf_url":"https://arxiv.org/pdf/2610.26610","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.2610.26610","doi":"https://doi.org/10.48550/arxiv.2610.26610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26610","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:2610.26610","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26610","pdf_url":"https://arxiv.org/pdf/2610.26610","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/W7223068643.pdf","grobid_xml":"https://content.openalex.org/works/W7223068643.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4414587641"],"related_works":["https://openalex.org/W7223272607","https://openalex.org/W4367188707","https://openalex.org/W1496974612","https://openalex.org/W4399151929","https://openalex.org/W4390271934","https://openalex.org/W3081693328","https://openalex.org/W2599845157","https://openalex.org/W7172533577","https://openalex.org/W4404644384","https://openalex.org/W3179762332"],"abstract_inverted_index":{"The":[0],"code":[1,115],"$\\{000,220,202,022\\}\\subset\\mathbb{Z}_4^3$":[2],"realizes":[3],"the":[4,15,19,30,60,73,85,89,110,113,117],"split":[5],"$A_3$":[6,28],"root-weight":[7],"gluing":[8,34,90,103],"construction":[9],"as":[10],"ordinary":[11],"Construction":[12],"A,":[13],"preserving":[14],"Lorentzian":[16],"pairing":[17],"and":[18,42,45],"positive":[20],"energy":[21],"form.":[22],"For":[23,70],"two":[24,64],"hyperbolic":[25],"pairs":[26],"of":[27,102],"blocks,":[29],"twenty-two":[31],"even":[32],"self-dual":[33],"codes":[35,104],"form":[36],"seven":[37,50],"block-monomial":[38],"classes.":[39],"Explicit":[40],"metric":[41],"$B$-field":[43],"representatives":[44],"theta":[46],"series":[47],"distinguish":[48],"exactly":[49],"T-duality":[51,99],"classes":[52,65],"in":[53,88],"this":[54],"family":[55,62],"at":[56,66],"central":[57,67],"charge":[58,68],"six;":[59],"one-pair":[61],"has":[63,96],"three.":[69],"arbitrary":[71],"$d$,":[72],"chiral":[74],"root":[75],"system":[76],"on":[77],"either":[78],"side":[79],"is":[80],"$A_1^{3m}$,":[81],"where":[82],"$m$":[83],"counts":[84],"words":[86],"$(2e_i,2e_i)$":[87],"code.":[91],"Exactly":[92],"one":[93],"two-pair":[94],"class":[95],"no":[97],"zero-$B$":[98],"frame.":[100],"Intersections":[101],"determine":[105],"finite":[106],"shift":[107],"orbifolds":[108],"between":[109],"backgrounds,":[111],"with":[112],"target":[114],"specifying":[116],"twisted-sector":[118],"projections.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}