{"id":"https://openalex.org/W7213397967","doi":"https://doi.org/10.48550/arxiv.2609.17359","title":"Topological Modular Forms Constrain Threshold States in Extremal $\\mathcal{N}=1$ AdS$_3$ Gravity","display_name":"Topological Modular Forms Constrain Threshold States in Extremal $\\mathcal{N}=1$ AdS$_3$ Gravity","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213397967","doi":"https://doi.org/10.48550/arxiv.2609.17359"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17359","pdf_url":"https://arxiv.org/pdf/2609.17359","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/2609.17359","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143400428","display_name":"Yutaka Yoshida","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I120043899","display_name":"Meiji Gakuin University","ror":"https://ror.org/01zwcys39","country_code":"JP","type":"education","lineage":["https://openalex.org/I120043899"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yoshida, Yutaka","raw_affiliation_strings":["Department of Current Legal Studies , Faculty of Law , Meiji Gakuin University , 1-2-37 Shirokanedai , Minato-ku , Tokyo 108-8636 , Japan","Institute for Mathematical Informatics , Meiji Gakuin University , 1518 Kamikurata-cho , Totsuka-ku , Yokohama 244-8539 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Current Legal Studies , Faculty of Law , Meiji Gakuin University , 1-2-37 Shirokanedai , Minato-ku , Tokyo 108-8636 , Japan","institution_ids":["https://openalex.org/I120043899"]},{"raw_affiliation_string":"Institute for Mathematical Informatics , Meiji Gakuin University , 1518 Kamikurata-cho , Totsuka-ku , Yokohama 244-8539 , Japan","institution_ids":["https://openalex.org/I120043899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5143400428"],"corresponding_institution_ids":["https://openalex.org/I120043899"],"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":0.9994999766349792,"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":0.9994999766349792,"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":0.0003000000142492354,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/topological-modular-forms","display_name":"topological modular forms","score":0.9789999723434448},{"id":"https://openalex.org/keywords/extremal-black-holes","display_name":"extremal black holes","score":0.6589999794960022},{"id":"https://openalex.org/keywords/n-1-supergravity","display_name":"N=1 supergravity","score":0.8410000205039978},{"id":"https://openalex.org/keywords/btz-black-hole","display_name":"BTZ black hole","score":0.8159999847412109},{"id":"https://openalex.org/keywords/threshold-states","display_name":"threshold states","score":0.7110000252723694},{"id":"https://openalex.org/keywords/modular-covariance","display_name":"modular covariance","score":0.5789999961853027},{"id":"https://openalex.org/keywords/central-charge","display_name":"central charge","score":0.9229999780654907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5591999888420105},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.49790000915527344},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C2778300598","wikidata":"https://www.wikidata.org/wiki/Q2638561","display_name":"General covariance","level":3,"score":0.40549999475479126},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.397599995136261},{"id":"https://openalex.org/C199793620","wikidata":"https://www.wikidata.org/wiki/Q7825030","display_name":"Topological degeneracy","level":5,"score":0.3952000141143799},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C2777345500","wikidata":"https://www.wikidata.org/wiki/Q3658596","display_name":"Central charge","level":3,"score":0.3666999936103821},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C527218924","wikidata":"https://www.wikidata.org/wiki/Q964053","display_name":"Topological algebra","level":3,"score":0.35569998621940613},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34389999508857727},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C97900337","wikidata":"https://www.wikidata.org/wiki/Q60367","display_name":"Modular invariance","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C180987920","wikidata":"https://www.wikidata.org/wiki/Q922339","display_name":"Topological ring","level":4,"score":0.2646999955177307},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17359","pdf_url":"https://arxiv.org/pdf/2609.17359","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.2609.17359","doi":"https://doi.org/10.48550/arxiv.2609.17359","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17359","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:2609.17359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17359","pdf_url":"https://arxiv.org/pdf/2609.17359","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213397967.pdf","grobid_xml":"https://content.openalex.org/works/W7213397967.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1524124868","https://openalex.org/W1668604913","https://openalex.org/W1763748250","https://openalex.org/W1820729294","https://openalex.org/W1872046492","https://openalex.org/W1972145497","https://openalex.org/W1975883511","https://openalex.org/W2090069870","https://openalex.org/W2127553322","https://openalex.org/W2330908629","https://openalex.org/W2534694177","https://openalex.org/W2898755291","https://openalex.org/W2898870077","https://openalex.org/W3023304147","https://openalex.org/W3164775110","https://openalex.org/W4317735673","https://openalex.org/W4323075891"],"related_works":["https://openalex.org/W2949370594","https://openalex.org/W2035651041","https://openalex.org/W4415938389","https://openalex.org/W2898870077","https://openalex.org/W7134067272","https://openalex.org/W4385959875","https://openalex.org/W4317735673","https://openalex.org/W7099143186","https://openalex.org/W2050966315","https://openalex.org/W2065262198"],"abstract_inverted_index":{"We":[0],"identify":[1],"a":[2],"topological":[3,29],"constraint":[4],"on":[5],"extremal":[6,51],"$\\mathcal{N}=1$":[7,53],"AdS$_3$":[8],"spectra":[9],"that":[10,40],"is":[11,76],"not":[12],"implied":[13],"by":[14],"genus-one":[15],"modular":[16,30],"covariance":[17],"of":[18,33,61],"the":[19,27,34,65,69],"three":[20],"even":[21],"spin":[22],"structure":[23],"partition":[24],"functions.":[25],"Assuming":[26],"expected":[28],"forms":[31],"divisibility":[32],"Ramond":[35],"Witten":[36],"index,":[37],"we":[38],"show":[39],"for":[41,78],"infinitely":[42],"many":[43],"odd":[44,59],"$n$":[45],"at":[46,64],"central":[47],"charge":[48],"$c=12n$,":[49],"an":[50,58],"holomorphic":[52],"superconformal":[54],"field":[55],"theory":[56],"requires":[57],"number":[60],"Neveu--Schwarz":[62],"primaries":[63,75],"BTZ":[66],"threshold.":[67],"Thus":[68],"strict":[70],"ansatz":[71],"with":[72],"no":[73],"threshold":[74],"excluded":[77],"this":[79],"infinite":[80],"family.":[81]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}
