{"id":"https://openalex.org/W2525300511","doi":"https://doi.org/10.48550/arxiv.1609.09320","title":"Phases of $\\mathcal{N}=4$ SYM, S-duality and Nilpotent Cones","display_name":"Phases of $\\mathcal{N}=4$ SYM, S-duality and Nilpotent Cones","publication_year":2016,"publication_date":"2016-09-29","ids":{"openalex":"https://openalex.org/W2525300511","doi":"https://doi.org/10.48550/arxiv.1609.09320","mag":"2525300511"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1609.09320","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09320","pdf_url":"https://arxiv.org/pdf/1609.09320","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/1609.09320","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082992014","display_name":"Aswin Balasubramanian","orcid":"https://orcid.org/0000-0001-6046-0779","observed_orcids":["https://orcid.org/0000-0001-6046-0779"]},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I2801876189","display_name":"Deutsches Elektronen-Synchrotron DESY","ror":"https://ror.org/01js2sh04","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2801876189"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Balasubramanian, Aswin","raw_affiliation_strings":["DESY Theory Notkestr . 85 22607 Hamburg","Department of Mathematics University of Hamburg Bundesstr. 55 20146 Hamburg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DESY Theory Notkestr . 85 22607 Hamburg","institution_ids":["https://openalex.org/I2801876189"]},{"raw_affiliation_string":"Department of Mathematics University of Hamburg Bundesstr. 55 20146 Hamburg","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082992014"],"corresponding_institution_ids":["https://openalex.org/I159176309","https://openalex.org/I2801876189"],"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9208999872207642,"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":0.9208999872207642,"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":0.052000001072883606,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.006000000052154064,"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/n-4-super-yang-mills","display_name":"N=4 supersymmetric Yang-Mills","score":0.9700000286102295},{"id":"https://openalex.org/keywords/stratified-spaces","display_name":"stratified spaces","score":0.7850000262260437},{"id":"https://openalex.org/keywords/s-duality","display_name":"S-duality","score":0.9259999990463257},{"id":"https://openalex.org/keywords/nilpotent-cone","display_name":"nilpotent cone","score":0.8989999890327454},{"id":"https://openalex.org/keywords/geometric-langlands-program","display_name":"geometric Langlands program","score":0.878000020980835},{"id":"https://openalex.org/keywords/compact-simple-lie-groups","display_name":"compact simple Lie groups","score":0.703000009059906},{"id":"https://openalex.org/keywords/effective-field-theory","display_name":"effective field theory","score":0.7730000019073486}],"concepts":[{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5612753629684448},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5463053584098816},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5160214900970459},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.49010786414146423},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4853910207748413},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4766567349433899},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4614485800266266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42709124088287354},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37832674384117126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35643771290779114},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3530246913433075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18684706091880798},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:1609.09320","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09320","pdf_url":"https://arxiv.org/pdf/1609.09320","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:bib-pubdb1.desy.de:309817","doi":null,"is_oa":true,"landing_page_url":"https://bib-pubdb1.desy.de/search?p=id:%22PUBDB-2016-03997%22","pdf_url":"https://bib-pubdb1.desy.de/record/309817","source":{"id":"https://openalex.org/S4306401389","display_name":"DESY (CERN, DESY, Fermilab, IHEP, and SLAC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"21 pp. (2016).","raw_type":"info:eu-repo/semantics/report"},{"id":"mag:2525300511","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1609.09320.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1609.09320","doi":"https://doi.org/10.48550/arxiv.1609.09320","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.09320","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.09320","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09320","pdf_url":"https://arxiv.org/pdf/1609.09320","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/W2525300511.pdf","grobid_xml":"https://content.openalex.org/works/W2525300511.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W606654790","https://openalex.org/W1494449975","https://openalex.org/W1531500295","https://openalex.org/W1540739244","https://openalex.org/W1571072992","https://openalex.org/W1906166394","https://openalex.org/W1940562746","https://openalex.org/W1966072442","https://openalex.org/W1976431822","https://openalex.org/W1987958994","https://openalex.org/W1998322527","https://openalex.org/W2006554783","https://openalex.org/W2019419934","https://openalex.org/W2045151304","https://openalex.org/W2062009667","https://openalex.org/W2065205663","https://openalex.org/W2067437844","https://openalex.org/W2067732336","https://openalex.org/W2071919968","https://openalex.org/W2083924347","https://openalex.org/W2084677432","https://openalex.org/W2104651181","https://openalex.org/W2106586200","https://openalex.org/W2112842519","https://openalex.org/W2116341229","https://openalex.org/W2148705192","https://openalex.org/W2465496826","https://openalex.org/W2527245325","https://openalex.org/W2593824906","https://openalex.org/W2946720308","https://openalex.org/W2952719166","https://openalex.org/W2963095086","https://openalex.org/W3099356683","https://openalex.org/W4297880366"],"related_works":["https://openalex.org/W1858203177","https://openalex.org/W2729833062","https://openalex.org/W2045992963","https://openalex.org/W7101050828","https://openalex.org/W7096272582","https://openalex.org/W7095959712","https://openalex.org/W2964187524","https://openalex.org/W2556586196","https://openalex.org/W7096834261","https://openalex.org/W2131158472"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"I":[3,83,90,131],"describe":[4],"the":[5,33,48,53,62,72,85,101,104,111,135,143,149,152,158,164,183],"space":[6,54,106],"of":[7,10,50,55,61,64,74,88,95,103,107,113,127,142,151],"vacua":[8,56,108],"$\\mathcal{V}$":[9],"four":[11,153],"dimensional":[12,154],"$\\mathcal{N}=4$":[13,65,116],"SYM":[14,66,117],"on":[15,110,118,148,171],"$\\mathbb{R}^4$":[16],"with":[17],"gauge":[18],"group":[19],"a":[20,27,77,98,119,172,179],"compact":[21],"simple":[22],"Lie":[23,78],"Group":[24],"$G$":[25],"as":[26,140],"stratified":[28],"space.":[29],"On":[30],"each":[31],"stratum,":[32],"low":[34],"energy":[35],"effective":[36],"field":[37],"theory":[38,73,155,165],"is":[39],"different.":[40],"This":[41],"language":[42,99],"allows":[43],"one":[44],"to":[45,168],"make":[46],"precise":[47],"idea":[49],"moving":[51],"in":[52,76,163,182],"$\\mathcal{V}$.":[57],"A":[58],"particular":[59],"subset":[60],"strata":[63],"can":[67],"be":[68],"efficiently":[69],"described":[70],"using":[71,96],"sheets":[75],"algebra.":[79],"For":[80],"these":[81],"strata,":[82],"study":[84,102],"conjectural":[86],"action":[87],"S-duality.":[89],"also":[91],"indicate":[92,132],"some":[93],"benefits":[94],"such":[97],"for":[100],"available":[105,144],"$\\overline{\\mathcal{V}}$":[109],"boundary":[112,128,150],"GL":[114],"twisted":[115],"half-space":[120],"$\\mathbb{R}^3":[121],"\\times":[122],"\\mathbb{R}^+$.":[123],"As":[124],"an":[125],"application":[126],"symmetry":[129,145],"breaking,":[130],"how":[133],"a)":[134],"Local":[136,184],"Nilpotent":[137,160],"Cone":[138,161],"arises":[139,162],"part":[141],"breaking":[146],"choices":[147],"and":[156,185],"b)":[157],"Global":[159,186],"reduced":[166],"down":[167],"two":[169],"dimensions":[170],"Riemann":[173],"Surface":[174],"$C$.":[175],"These":[176],"geometries":[177],"play":[178],"critical":[180],"role":[181],"Geometric":[187],"Langlands":[188],"Program(s).":[189]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-10-07T00:00:00"}