{"id":"https://openalex.org/W7214053201","doi":"https://doi.org/10.48550/arxiv.2609.24551","title":"Dirac-harmonic maps from manifolds with boundary via index theory","display_name":"Dirac-harmonic maps from manifolds with boundary via index theory","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214053201","doi":"https://doi.org/10.48550/arxiv.2609.24551"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24551","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24551","pdf_url":"https://arxiv.org/pdf/2609.24551","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/2609.24551","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051971206","display_name":"Volker Branding","orcid":"https://orcid.org/0000-0002-1535-1474","observed_orcids":["https://orcid.org/0000-0002-1535-1474"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Branding, Volker","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041625585","display_name":"Nicolas Ginoux","orcid":"https://orcid.org/0000-0003-4843-4644","observed_orcids":["https://orcid.org/0000-0003-4843-4644"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"Ginoux, Nicolas","raw_affiliation_strings":["University of Rostock , Institute of Mathematics , Ulmenstra\u00dfe 69 , 18057 Rostock , Germany","Universit\u00e9 de Lorraine , CNRS , IECL , F-57000 Metz , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rostock , Institute of Mathematics , Ulmenstra\u00dfe 69 , 18057 Rostock , Germany","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine , CNRS , IECL , F-57000 Metz , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7310000061988831,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7310000061988831,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.07069999724626541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12351","display_name":"Geometry and complex manifolds","score":0.05469999834895134,"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/dirac-harmonic-maps","display_name":"Dirac-harmonic maps","score":0.9990000128746033},{"id":"https://openalex.org/keywords/supersymmetric-sigma-models","display_name":"supersymmetric sigma models","score":0.8539999723434448},{"id":"https://openalex.org/keywords/atiyah-patodi-singer-index-theorem","display_name":"Atiyah-Patodi-Singer index theorem","score":0.8410000205039978},{"id":"https://openalex.org/keywords/manifolds-with-boundary","display_name":"manifolds with boundary","score":0.9430000185966492},{"id":"https://openalex.org/keywords/existence-of-critical-points","display_name":"existence of critical points","score":0.902999997138977},{"id":"https://openalex.org/keywords/twistor-spinors","display_name":"twistor spinors","score":0.9210000038146973},{"id":"https://openalex.org/keywords/surfaces","display_name":"surfaces","score":0.640999972820282}],"concepts":[{"id":"https://openalex.org/C25793852","wikidata":"https://www.wikidata.org/wiki/Q279082","display_name":"Twistor theory","level":2,"score":0.6855999827384949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6841999888420105},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6557999849319458},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.5241000056266785},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5081999897956848},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4927000105381012},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4659000039100647},{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.4171999990940094},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3797999918460846},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30239999294281006},{"id":"https://openalex.org/C15349852","wikidata":"https://www.wikidata.org/wiki/Q7858591","display_name":"Twistor space","level":3,"score":0.3021000027656555},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.24551","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24551","pdf_url":"https://arxiv.org/pdf/2609.24551","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":"pmh:oai:HAL:hal-05757916v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05757916v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.24551","doi":"https://doi.org/10.48550/arxiv.2609.24551","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24551","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24551","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24551","pdf_url":"https://arxiv.org/pdf/2609.24551","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/W7214053201.pdf","grobid_xml":"https://content.openalex.org/works/W7214053201.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4297677062","https://openalex.org/W7127153520","https://openalex.org/W7128613995"],"related_works":["https://openalex.org/W2019846587","https://openalex.org/W4403738359","https://openalex.org/W2076446452","https://openalex.org/W2108114113","https://openalex.org/W1845598337","https://openalex.org/W2955048405","https://openalex.org/W3144381239","https://openalex.org/W2016761049","https://openalex.org/W1968469215","https://openalex.org/W2488506031"],"abstract_inverted_index":{"Dirac-harmonic":[0],"maps":[1],"are":[2,69,99],"a":[3,29,43,66,79],"mathematical":[4],"version":[5],"of":[6,12,22,65],"the":[7,63,73,84],"supersymmetric":[8],"non-linear":[9],"sigma":[10],"model":[11],"quantum":[13],"field":[14],"theory.":[15],"Since":[16],"they":[17],"arise":[18],"as":[19],"critical":[20],"points":[21],"an":[23],"unbounded":[24],"energy":[25],"functional,":[26],"it":[27,57],"is":[28,83],"challenging":[30],"task":[31],"to":[32,62],"establish":[33],"general":[34,44],"existence":[35,45],"results.":[36],"Within":[37],"this":[38],"manuscript":[39],"we":[40],"mainly":[41],"prove":[42],"result":[46],"based":[47,93],"on":[48,94,97],"index":[49,75],"theory":[50],"for":[51,78],"manifolds":[52],"with":[53],"boundary":[54,67],"and":[55],"apply":[56],"in":[58,72,87],"various":[59],"situations.":[60],"Due":[61],"presence":[64],"there":[68],"additional":[70],"contributions":[71],"Atiyah-Patodi-Singer":[74],"formula":[76],"allowing":[77],"non-vanishing":[80],"index,":[81],"which":[82],"key":[85],"argument":[86],"our":[88],"proofs.":[89],"Further":[90],"explicit":[91],"examples":[92],"twistor":[95],"spinors":[96],"surfaces":[98],"also":[100],"presented.":[101]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}