{"id":"https://openalex.org/W3065587336","doi":"https://doi.org/10.1007/jhep12(2020)126","title":"Resolving modular flow: a toolkit for free fermions","display_name":"Resolving modular flow: a toolkit for free fermions","publication_year":2020,"publication_date":"2020-12-01","ids":{"openalex":"https://openalex.org/W3065587336","doi":"https://doi.org/10.1007/jhep12(2020)126","mag":"3065587336"},"language":"en","primary_location":{"id":"doi:10.1007/jhep12(2020)126","doi":"https://doi.org/10.1007/jhep12(2020)126","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep12(2020)126","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP12(2020)126.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/JHEP12(2020)126.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078581746","display_name":"Johanna Erdmenger B","orcid":"https://orcid.org/0000-0003-4776-4326","observed_orcids":["https://orcid.org/0000-0003-4776-4326"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johanna Erdmenger","raw_affiliation_strings":["Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Pascal Fries","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pascal Fries","raw_affiliation_strings":["Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087838300","display_name":"Ignacio A. Reyes","orcid":"https://orcid.org/0000-0001-5456-5590","observed_orcids":["https://orcid.org/0000-0001-5456-5590"]},"institutions":[{"id":"https://openalex.org/I4210127646","display_name":"Max Planck Institute for Gravitational Physics","ror":"https://ror.org/03sry2h30","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127646"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ignacio A. Reyes","raw_affiliation_strings":["Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am M\u00fchlenberg 1, 14476, Potsdam-Golm, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5456-5590","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am M\u00fchlenberg 1, 14476, Potsdam-Golm, Germany","institution_ids":["https://openalex.org/I4210127646"]}]},{"author_position":"last","author":{"id":null,"display_name":"Christian P. Simon","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian P. Simon","raw_affiliation_strings":["Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universit\u00e4t W\u00fcrzburg, Am Hubland, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087838300"],"corresponding_institution_ids":["https://openalex.org/I4210127646"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.9996,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.7424792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"2020","issue":"12","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":0.6050000190734863,"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":0.6050000190734863,"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/T11804","display_name":"Quantum many-body systems","score":0.21899999678134918,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.08590000122785568,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/modular-flow","display_name":"modular flow","score":0.9929999709129333},{"id":"https://openalex.org/keywords/resolvent","display_name":"resolvent","score":0.781000018119812},{"id":"https://openalex.org/keywords/kms-condition","display_name":"KMS condition","score":0.9559999704360962},{"id":"https://openalex.org/keywords/modular-evolution","display_name":"modular evolution","score":0.7179999947547913},{"id":"https://openalex.org/keywords/entanglement","display_name":"entanglement","score":0.7770000100135803},{"id":"https://openalex.org/keywords/modular-symmetry","display_name":"modular symmetry","score":0.3370000123977661},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.5429999828338623},{"id":"https://openalex.org/keywords/cylinder","display_name":"cylinder","score":0.9660000205039978},{"id":"https://openalex.org/keywords/temperature-dependence","display_name":"temperature dependence","score":0.4230000078678131},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.7639999985694885}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8151000142097473},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6305999755859375},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.565500020980835},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.5325999855995178},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.520799994468689},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4449999928474426},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C97900337","wikidata":"https://www.wikidata.org/wiki/Q60367","display_name":"Modular invariance","level":3,"score":0.3643999993801117},{"id":"https://openalex.org/C181633103","wikidata":"https://www.wikidata.org/wiki/Q1834342","display_name":"Modular group","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3382999897003174},{"id":"https://openalex.org/C192423722","wikidata":"https://www.wikidata.org/wiki/Q1455736","display_name":"Global symmetry","level":4,"score":0.33399999141693115},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C54613284","wikidata":"https://www.wikidata.org/wiki/Q1191271","display_name":"Conformal field theory","level":3,"score":0.3255999982357025},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2709999978542328},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C101454708","wikidata":"https://www.wikidata.org/wiki/Q17106019","display_name":"Standard Model (mathematical formulation)","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C173848574","wikidata":"https://www.wikidata.org/wiki/Q3507963","display_name":"Conformal symmetry","level":3,"score":0.2599000036716461},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/jhep12(2020)126","doi":"https://doi.org/10.1007/jhep12(2020)126","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep12(2020)126","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP12(2020)126.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2008.07532","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.07532","pdf_url":"https://arxiv.org/pdf/2008.07532","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:doaj.org/article:3e9a5dbf4ce24255abfd729edf71b62e","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/3e9a5dbf4ce24255abfd729edf71b62e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of High Energy Physics, Vol 2020, Iss 12, Pp 1-32 (2020)","raw_type":"article"},{"id":"pmh:oai:pure.mpg.de:item_3250945","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0006-F2CF-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of High Energy Physics","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2008.07532","doi":"https://doi.org/10.48550/arxiv.2008.07532","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2008.07532","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/jhep12(2020)126","doi":"https://doi.org/10.1007/jhep12(2020)126","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep12(2020)126","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP12(2020)126.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7404924790","display_name":null,"funder_award_id":"HI 744/9-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3065587336.pdf","grobid_xml":"https://content.openalex.org/works/W3065587336.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W1524878283","https://openalex.org/W1564938723","https://openalex.org/W1743754552","https://openalex.org/W1882863446","https://openalex.org/W1967300267","https://openalex.org/W1976421249","https://openalex.org/W1989074507","https://openalex.org/W2009097480","https://openalex.org/W2024382141","https://openalex.org/W2042161903","https://openalex.org/W2050368830","https://openalex.org/W2055569491","https://openalex.org/W2059799037","https://openalex.org/W2076259017","https://openalex.org/W2076443407","https://openalex.org/W2086836656","https://openalex.org/W2110283120","https://openalex.org/W2113401645","https://openalex.org/W2114561881","https://openalex.org/W2116423251","https://openalex.org/W2139275006","https://openalex.org/W2143285639","https://openalex.org/W2151993464","https://openalex.org/W2157169018","https://openalex.org/W2171842910","https://openalex.org/W2270074405","https://openalex.org/W2400443327","https://openalex.org/W2482618801","https://openalex.org/W2494415787","https://openalex.org/W2586549544","https://openalex.org/W2604578214","https://openalex.org/W2607094525","https://openalex.org/W2610776282","https://openalex.org/W2728552031","https://openalex.org/W2770939712","https://openalex.org/W2776227488","https://openalex.org/W2790814557","https://openalex.org/W2803739589","https://openalex.org/W2810868271","https://openalex.org/W2892123151","https://openalex.org/W2896923555","https://openalex.org/W2901517632","https://openalex.org/W2901784132","https://openalex.org/W2903708277","https://openalex.org/W2939608477","https://openalex.org/W2946249006","https://openalex.org/W2946392624","https://openalex.org/W2948718542","https://openalex.org/W2951999874","https://openalex.org/W2952789760","https://openalex.org/W2954852213","https://openalex.org/W2990147705","https://openalex.org/W2992617487","https://openalex.org/W3006259251","https://openalex.org/W3030260765","https://openalex.org/W3099309741","https://openalex.org/W3100823004","https://openalex.org/W3100909180","https://openalex.org/W3101533176","https://openalex.org/W4206688401"],"related_works":["https://openalex.org/W4383619629","https://openalex.org/W2803508302","https://openalex.org/W7128516172","https://openalex.org/W2951999874","https://openalex.org/W4312191550","https://openalex.org/W4411251842","https://openalex.org/W2939608477","https://openalex.org/W3106806761","https://openalex.org/W4400142012","https://openalex.org/W2890140742"],"abstract_inverted_index":{"Abstract":[0],"Modular":[1],"flow":[2],"is":[3,37,52,136],"a":[4,23,55,75],"symmetry":[5,90],"of":[6,9,49,122],"the":[7,73,96,120,129,141,157],"algebra":[8],"observables":[10],"associated":[11],"to":[12,18,53,115,119,155],"space-time":[13],"regions.":[14],"Being":[15],"closely":[16],"related":[17],"entanglement,":[19],"it":[20],"has":[21],"played":[22],"key":[24,47],"role":[25],"in":[26,65,78,117,137],"recent":[27],"connections":[28],"between":[29,159],"information":[30],"theory,":[31],"QFT":[32],"and":[33,99,104,161],"gravity.":[34],"However,":[35],"little":[36],"known":[38],"about":[39],"its":[40],"action":[41],"beyond":[42],"highly":[43],"symmetric":[44],"cases.":[45],"The":[46],"idea":[48],"this":[50],"work":[51],"introduce":[54],"new":[56,153],"formula":[57],"for":[58,61,92],"modular":[59,130,146],"flows":[60],"free":[62],"chiral":[63],"fermions":[64],"1":[66,68],"+":[67],"dimensions,":[69],"working":[70],"directly":[71],"from":[72,112],"resolvent,":[74],"standard":[76],"technique":[77],"complex":[79],"analysis.":[80],"We":[81,127],"present":[82],"novel":[83],"results":[84],"\u2014":[85,91],"not":[86],"fixed":[87],"by":[88],"conformal":[89],"disjoint":[93],"regions":[94],"on":[95,102],"plane,":[97],"cylinder":[98],"torus.":[100],"Depending":[101],"temperature":[103],"boundary":[105],"conditions,":[106],"these":[107],"display":[108],"different":[109],"behaviour":[110],"ranging":[111],"purely":[113],"local":[114],"non-local":[116],"relation":[118],"mixing":[121],"operators":[123],"at":[124],"spacelike":[125],"separation.":[126],"find":[128],"two-point":[131],"function,":[132],"whose":[133],"analytic":[134],"structure":[135],"precise":[138],"agreement":[139],"with":[140],"KMS":[142],"condition":[143],"that":[144],"governs":[145],"evolution.":[147],"Our":[148],"ready-to-use":[149],"formulae":[150],"may":[151],"provide":[152],"ingredients":[154],"explore":[156],"connection":[158],"spacetime":[160],"entanglement.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2021,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-08-24T00:00:00"}
