Dessins d’enfants, Seiberg-Witten curves and conformal blocks View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2021-05-10

AUTHORS

Jiakang Bao, Omar Foda, Yang-Hui He, Edward Hirst, James Read, Yan Xiao, Futoshi Yagi

ABSTRACT

We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models. More... »

PAGES

65

References to SciGraph publications

  • 2015-06-12. 5d En Seiberg-Witten curve via toric-like diagram in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-30. Non-Lagrangian theories from brane junctions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-09-24. The Topological Vertex in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2013-11-13. Refined stable pair invariants for E-, M- and [p, q]-strings in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-08-17. Dessins d’enfants in N=2 generalised quiver theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1994-10. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-07-24. From topological strings to minimal models in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-03-25. 5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-22. Eta products, BPS states and K3 surfaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-07-04. Conformal blocks of WN minimal models and AGT correspondence in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-08-06. N = 2 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2017-01-23. Equivalence of several descriptions for 6d SCFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02-05. Penner type matrix model and Seiberg-Witten theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-03-17. Refined topological vertex and instanton counting in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-22. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2014-06-30. AGT, Burge pairs and minimal models in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-10-26. The refined topological vertex in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-07-13. General instanton counting and 5d SCFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-04-20. M5-branes, toric diagrams and gauge theory duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-01-06. Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-01-01. Seiberg-Witten Theory and Random Partitions in THE UNITY OF MATHEMATICS
  • 2014-06-03. Topological strings and 5d TN partition functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-11-03. The Ω Deformed B-model for Rigid N = 2 Theories in ANNALES HENRI POINCARÉ
  • 2005-05-17. Instanton counting, Macdonald function and the moduli space of D-branes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-08-09. A& B model approaches to surface operators and Toda thoeries in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-16. Discrete θ and the 5d superconformal index in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep05(2021)065

    DOI

    http://dx.doi.org/10.1007/jhep05(2021)065

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1137937243


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Department of Mathematics, City, University of London, EC1V 0HB, London, U.K."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Bao", 
            "givenName": "Jiakang", 
            "id": "sg:person.011124215003.75", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011124215003.75"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematics and Statistics, University of Melbourne, Royal Parade, 3010, Parkville, VIC, Australia", 
              "id": "http://www.grid.ac/institutes/grid.1008.9", 
              "name": [
                "School of Mathematics and Statistics, University of Melbourne, Royal Parade, 3010, Parkville, VIC, Australia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Foda", 
            "givenName": "Omar", 
            "id": "sg:person.013247432110.94", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013247432110.94"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Physics, NanKai University, 300071, Tianjin, P.R. China", 
              "id": "http://www.grid.ac/institutes/grid.216938.7", 
              "name": [
                "Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.", 
                "Merton College, University of Oxford, OX1 4JD, Oxford, U.K.", 
                "London Institute of Mathematical Sciences, 35a South St, Mayfair, W1K 2XF, London, U.K.", 
                "School of Physics, NanKai University, 300071, Tianjin, P.R. China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "He", 
            "givenName": "Yang-Hui", 
            "id": "sg:person.010540777615.39", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010540777615.39"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Department of Mathematics, City, University of London, EC1V 0HB, London, U.K."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hirst", 
            "givenName": "Edward", 
            "id": "sg:person.016633230541.26", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016633230541.26"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Pembroke College, University of Oxford, OX1 1DW, Oxford, U.K.", 
              "id": "http://www.grid.ac/institutes/grid.4991.5", 
              "name": [
                "Pembroke College, University of Oxford, OX1 1DW, Oxford, U.K."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Read", 
            "givenName": "James", 
            "id": "sg:person.014070635676.32", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014070635676.32"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Physics, Tsinghua University, 100084, Beijing, China", 
              "id": "http://www.grid.ac/institutes/grid.12527.33", 
              "name": [
                "Department of Physics, Tsinghua University, 100084, Beijing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Xiao", 
            "givenName": "Yan", 
            "id": "sg:person.015450711333.47", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015450711333.47"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematics, Southwest Jiaotong University, West Zone, High-Tech District, 611756, Chengdu, Sichuan, China", 
              "id": "http://www.grid.ac/institutes/grid.263901.f", 
              "name": [
                "School of Mathematics, Southwest Jiaotong University, West Zone, High-Tech District, 611756, Chengdu, Sichuan, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yagi", 
            "givenName": "Futoshi", 
            "id": "sg:person.012106514747.79", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012106514747.79"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/jhep11(2013)112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035823476", 
              "https://doi.org/10.1007/jhep11(2013)112"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099774", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049578045", 
              "https://doi.org/10.1007/bf02099774"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2017)093", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1074205037", 
              "https://doi.org/10.1007/jhep01(2017)093"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2012)034", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000072911", 
              "https://doi.org/10.1007/jhep08(2012)034"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/10/069", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012019814", 
              "https://doi.org/10.1088/1126-6708/2009/10/069"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2015)082", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049877267", 
              "https://doi.org/10.1007/jhep06(2015)082"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/1998/01/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026223761", 
              "https://doi.org/10.1088/1126-6708/1998/01/002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2014)113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004223466", 
              "https://doi.org/10.1007/jhep01(2014)113"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043144023", 
              "https://doi.org/10.1007/jhep02(2010)022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2014)024", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049369773", 
              "https://doi.org/10.1007/jhep07(2014)024"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2014)112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038757919", 
              "https://doi.org/10.1007/jhep03(2014)112"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00023-012-0192-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024875783", 
              "https://doi.org/10.1007/s00023-012-0192-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2008/03/048", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059132731", 
              "https://doi.org/10.1088/1126-6708/2008/03/048"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2014)079", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028569668", 
              "https://doi.org/10.1007/jhep01(2014)079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2014)177", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052327494", 
              "https://doi.org/10.1007/jhep06(2014)177"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2014)175", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045230132", 
              "https://doi.org/10.1007/jhep01(2014)175"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2010)042", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033175317", 
              "https://doi.org/10.1007/jhep08(2010)042"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2012)105", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053174488", 
              "https://doi.org/10.1007/jhep04(2012)105"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2014)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041020676", 
              "https://doi.org/10.1007/jhep06(2014)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-004-1162-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047832310", 
              "https://doi.org/10.1007/s00220-004-1162-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2015)085", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043792581", 
              "https://doi.org/10.1007/jhep08(2015)085"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/0-8176-4467-9_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035404476", 
              "https://doi.org/10.1007/0-8176-4467-9_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-010-0369-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022882223", 
              "https://doi.org/10.1007/s11005-010-0369-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2015)063", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016122204", 
              "https://doi.org/10.1007/jhep07(2015)063"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2015)136", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003566313", 
              "https://doi.org/10.1007/jhep07(2015)136"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2005/05/039", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031122920", 
              "https://doi.org/10.1088/1126-6708/2005/05/039"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2021-05-10", 
        "datePublishedReg": "2021-05-10", 
        "description": "We show how to map Grothendieck\u2019s dessins d\u2019enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d N\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/jhep05(2021)065", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2021"
          }
        ], 
        "keywords": [
          "Seiberg-Witten curve", 
          "conformal blocks", 
          "instanton partition functions", 
          "algebraic curves", 
          "mirror map", 
          "Virasoro conformal blocks", 
          "gauge theory", 
          "dessins d\u2019enfants", 
          "partition function", 
          "minimal model", 
          "certain duality", 
          "d\u2019enfants", 
          "dessins", 
          "Grothendieck", 
          "duality", 
          "certain rules", 
          "parametrization", 
          "theory", 
          "curves", 
          "maps", 
          "model", 
          "sphere", 
          "function", 
          "rules", 
          "block", 
          "trivalent", 
          "puncture", 
          "AGT map", 
          "supersymmetric instanton partition functions", 
          "different minimal models"
        ], 
        "name": "Dessins d\u2019enfants, Seiberg-Witten curves and conformal blocks", 
        "pagination": "65", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1137937243"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep05(2021)065"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep05(2021)065", 
          "https://app.dimensions.ai/details/publication/pub.1137937243"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T19:02", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_885.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/jhep05(2021)065"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2021)065'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2021)065'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2021)065'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2021)065'


     

    This table displays all metadata directly associated to this object as RDF triples.

    252 TRIPLES      22 PREDICATES      81 URIs      47 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep05(2021)065 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N207c988f78c046358b29395572b88d58
    4 schema:citation sg:pub.10.1007/0-8176-4467-9_15
    5 sg:pub.10.1007/bf02099774
    6 sg:pub.10.1007/jhep01(2014)079
    7 sg:pub.10.1007/jhep01(2014)113
    8 sg:pub.10.1007/jhep01(2014)175
    9 sg:pub.10.1007/jhep01(2017)093
    10 sg:pub.10.1007/jhep02(2010)022
    11 sg:pub.10.1007/jhep03(2014)112
    12 sg:pub.10.1007/jhep04(2012)105
    13 sg:pub.10.1007/jhep06(2014)014
    14 sg:pub.10.1007/jhep06(2014)177
    15 sg:pub.10.1007/jhep06(2015)082
    16 sg:pub.10.1007/jhep07(2014)024
    17 sg:pub.10.1007/jhep07(2015)063
    18 sg:pub.10.1007/jhep07(2015)136
    19 sg:pub.10.1007/jhep08(2010)042
    20 sg:pub.10.1007/jhep08(2012)034
    21 sg:pub.10.1007/jhep08(2015)085
    22 sg:pub.10.1007/jhep11(2013)112
    23 sg:pub.10.1007/s00023-012-0192-x
    24 sg:pub.10.1007/s00220-004-1162-z
    25 sg:pub.10.1007/s11005-010-0369-5
    26 sg:pub.10.1088/1126-6708/1998/01/002
    27 sg:pub.10.1088/1126-6708/2005/05/039
    28 sg:pub.10.1088/1126-6708/2008/03/048
    29 sg:pub.10.1088/1126-6708/2009/10/069
    30 schema:datePublished 2021-05-10
    31 schema:datePublishedReg 2021-05-10
    32 schema:description We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.
    33 schema:genre article
    34 schema:inLanguage en
    35 schema:isAccessibleForFree true
    36 schema:isPartOf N7c16a0ac7b3749be938bbb558ffa21ce
    37 Nbfadd0eece9d451397dc4738266e32d1
    38 sg:journal.1052482
    39 schema:keywords AGT map
    40 Grothendieck
    41 Seiberg-Witten curve
    42 Virasoro conformal blocks
    43 algebraic curves
    44 block
    45 certain duality
    46 certain rules
    47 conformal blocks
    48 curves
    49 dessins
    50 dessins d’enfants
    51 different minimal models
    52 duality
    53 d’enfants
    54 function
    55 gauge theory
    56 instanton partition functions
    57 maps
    58 minimal model
    59 mirror map
    60 model
    61 parametrization
    62 partition function
    63 puncture
    64 rules
    65 sphere
    66 supersymmetric instanton partition functions
    67 theory
    68 trivalent
    69 schema:name Dessins d’enfants, Seiberg-Witten curves and conformal blocks
    70 schema:pagination 65
    71 schema:productId Ne4c827a58916431b894c6856ff80ff4d
    72 Neac475db4aeb409c96aaec045d375aca
    73 schema:sameAs https://app.dimensions.ai/details/publication/pub.1137937243
    74 https://doi.org/10.1007/jhep05(2021)065
    75 schema:sdDatePublished 2022-01-01T19:02
    76 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    77 schema:sdPublisher Nd687f089d9cc41118dddba55de394931
    78 schema:url https://doi.org/10.1007/jhep05(2021)065
    79 sgo:license sg:explorer/license/
    80 sgo:sdDataset articles
    81 rdf:type schema:ScholarlyArticle
    82 N207c988f78c046358b29395572b88d58 rdf:first sg:person.011124215003.75
    83 rdf:rest N989fdd47221d4035a11c07281b820807
    84 N729cc8caae3f4acb82ab60ad33f6cf4a rdf:first sg:person.014070635676.32
    85 rdf:rest Nf63283d9b84e4665a7ec1c082ef019e1
    86 N7c16a0ac7b3749be938bbb558ffa21ce schema:volumeNumber 2021
    87 rdf:type schema:PublicationVolume
    88 N8b51cf9d20934ff9b0a8c9c5fc6b81ad rdf:first sg:person.016633230541.26
    89 rdf:rest N729cc8caae3f4acb82ab60ad33f6cf4a
    90 N989fdd47221d4035a11c07281b820807 rdf:first sg:person.013247432110.94
    91 rdf:rest Nc6975910fc8c4da3b2a5cf0f6186f667
    92 Nbfadd0eece9d451397dc4738266e32d1 schema:issueNumber 5
    93 rdf:type schema:PublicationIssue
    94 Nc6975910fc8c4da3b2a5cf0f6186f667 rdf:first sg:person.010540777615.39
    95 rdf:rest N8b51cf9d20934ff9b0a8c9c5fc6b81ad
    96 Nd687f089d9cc41118dddba55de394931 schema:name Springer Nature - SN SciGraph project
    97 rdf:type schema:Organization
    98 Nd75a30822e344a9d96f9e8832ff3f169 rdf:first sg:person.012106514747.79
    99 rdf:rest rdf:nil
    100 Ne4c827a58916431b894c6856ff80ff4d schema:name doi
    101 schema:value 10.1007/jhep05(2021)065
    102 rdf:type schema:PropertyValue
    103 Neac475db4aeb409c96aaec045d375aca schema:name dimensions_id
    104 schema:value pub.1137937243
    105 rdf:type schema:PropertyValue
    106 Nf63283d9b84e4665a7ec1c082ef019e1 rdf:first sg:person.015450711333.47
    107 rdf:rest Nd75a30822e344a9d96f9e8832ff3f169
    108 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    109 schema:name Mathematical Sciences
    110 rdf:type schema:DefinedTerm
    111 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    112 schema:name Pure Mathematics
    113 rdf:type schema:DefinedTerm
    114 sg:journal.1052482 schema:issn 1029-8479
    115 1126-6708
    116 schema:name Journal of High Energy Physics
    117 schema:publisher Springer Nature
    118 rdf:type schema:Periodical
    119 sg:person.010540777615.39 schema:affiliation grid-institutes:grid.216938.7
    120 schema:familyName He
    121 schema:givenName Yang-Hui
    122 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010540777615.39
    123 rdf:type schema:Person
    124 sg:person.011124215003.75 schema:affiliation grid-institutes:None
    125 schema:familyName Bao
    126 schema:givenName Jiakang
    127 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011124215003.75
    128 rdf:type schema:Person
    129 sg:person.012106514747.79 schema:affiliation grid-institutes:grid.263901.f
    130 schema:familyName Yagi
    131 schema:givenName Futoshi
    132 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012106514747.79
    133 rdf:type schema:Person
    134 sg:person.013247432110.94 schema:affiliation grid-institutes:grid.1008.9
    135 schema:familyName Foda
    136 schema:givenName Omar
    137 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013247432110.94
    138 rdf:type schema:Person
    139 sg:person.014070635676.32 schema:affiliation grid-institutes:grid.4991.5
    140 schema:familyName Read
    141 schema:givenName James
    142 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014070635676.32
    143 rdf:type schema:Person
    144 sg:person.015450711333.47 schema:affiliation grid-institutes:grid.12527.33
    145 schema:familyName Xiao
    146 schema:givenName Yan
    147 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015450711333.47
    148 rdf:type schema:Person
    149 sg:person.016633230541.26 schema:affiliation grid-institutes:None
    150 schema:familyName Hirst
    151 schema:givenName Edward
    152 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016633230541.26
    153 rdf:type schema:Person
    154 sg:pub.10.1007/0-8176-4467-9_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035404476
    155 https://doi.org/10.1007/0-8176-4467-9_15
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/bf02099774 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049578045
    158 https://doi.org/10.1007/bf02099774
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/jhep01(2014)079 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028569668
    161 https://doi.org/10.1007/jhep01(2014)079
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1007/jhep01(2014)113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004223466
    164 https://doi.org/10.1007/jhep01(2014)113
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1007/jhep01(2014)175 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045230132
    167 https://doi.org/10.1007/jhep01(2014)175
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/jhep01(2017)093 schema:sameAs https://app.dimensions.ai/details/publication/pub.1074205037
    170 https://doi.org/10.1007/jhep01(2017)093
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/jhep02(2010)022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043144023
    173 https://doi.org/10.1007/jhep02(2010)022
    174 rdf:type schema:CreativeWork
    175 sg:pub.10.1007/jhep03(2014)112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038757919
    176 https://doi.org/10.1007/jhep03(2014)112
    177 rdf:type schema:CreativeWork
    178 sg:pub.10.1007/jhep04(2012)105 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053174488
    179 https://doi.org/10.1007/jhep04(2012)105
    180 rdf:type schema:CreativeWork
    181 sg:pub.10.1007/jhep06(2014)014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041020676
    182 https://doi.org/10.1007/jhep06(2014)014
    183 rdf:type schema:CreativeWork
    184 sg:pub.10.1007/jhep06(2014)177 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052327494
    185 https://doi.org/10.1007/jhep06(2014)177
    186 rdf:type schema:CreativeWork
    187 sg:pub.10.1007/jhep06(2015)082 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049877267
    188 https://doi.org/10.1007/jhep06(2015)082
    189 rdf:type schema:CreativeWork
    190 sg:pub.10.1007/jhep07(2014)024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049369773
    191 https://doi.org/10.1007/jhep07(2014)024
    192 rdf:type schema:CreativeWork
    193 sg:pub.10.1007/jhep07(2015)063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016122204
    194 https://doi.org/10.1007/jhep07(2015)063
    195 rdf:type schema:CreativeWork
    196 sg:pub.10.1007/jhep07(2015)136 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003566313
    197 https://doi.org/10.1007/jhep07(2015)136
    198 rdf:type schema:CreativeWork
    199 sg:pub.10.1007/jhep08(2010)042 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033175317
    200 https://doi.org/10.1007/jhep08(2010)042
    201 rdf:type schema:CreativeWork
    202 sg:pub.10.1007/jhep08(2012)034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000072911
    203 https://doi.org/10.1007/jhep08(2012)034
    204 rdf:type schema:CreativeWork
    205 sg:pub.10.1007/jhep08(2015)085 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043792581
    206 https://doi.org/10.1007/jhep08(2015)085
    207 rdf:type schema:CreativeWork
    208 sg:pub.10.1007/jhep11(2013)112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035823476
    209 https://doi.org/10.1007/jhep11(2013)112
    210 rdf:type schema:CreativeWork
    211 sg:pub.10.1007/s00023-012-0192-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1024875783
    212 https://doi.org/10.1007/s00023-012-0192-x
    213 rdf:type schema:CreativeWork
    214 sg:pub.10.1007/s00220-004-1162-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1047832310
    215 https://doi.org/10.1007/s00220-004-1162-z
    216 rdf:type schema:CreativeWork
    217 sg:pub.10.1007/s11005-010-0369-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022882223
    218 https://doi.org/10.1007/s11005-010-0369-5
    219 rdf:type schema:CreativeWork
    220 sg:pub.10.1088/1126-6708/1998/01/002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026223761
    221 https://doi.org/10.1088/1126-6708/1998/01/002
    222 rdf:type schema:CreativeWork
    223 sg:pub.10.1088/1126-6708/2005/05/039 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031122920
    224 https://doi.org/10.1088/1126-6708/2005/05/039
    225 rdf:type schema:CreativeWork
    226 sg:pub.10.1088/1126-6708/2008/03/048 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059132731
    227 https://doi.org/10.1088/1126-6708/2008/03/048
    228 rdf:type schema:CreativeWork
    229 sg:pub.10.1088/1126-6708/2009/10/069 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012019814
    230 https://doi.org/10.1088/1126-6708/2009/10/069
    231 rdf:type schema:CreativeWork
    232 grid-institutes:None schema:alternateName Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.
    233 schema:name Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.
    234 rdf:type schema:Organization
    235 grid-institutes:grid.1008.9 schema:alternateName School of Mathematics and Statistics, University of Melbourne, Royal Parade, 3010, Parkville, VIC, Australia
    236 schema:name School of Mathematics and Statistics, University of Melbourne, Royal Parade, 3010, Parkville, VIC, Australia
    237 rdf:type schema:Organization
    238 grid-institutes:grid.12527.33 schema:alternateName Department of Physics, Tsinghua University, 100084, Beijing, China
    239 schema:name Department of Physics, Tsinghua University, 100084, Beijing, China
    240 rdf:type schema:Organization
    241 grid-institutes:grid.216938.7 schema:alternateName School of Physics, NanKai University, 300071, Tianjin, P.R. China
    242 schema:name Department of Mathematics, City, University of London, EC1V 0HB, London, U.K.
    243 London Institute of Mathematical Sciences, 35a South St, Mayfair, W1K 2XF, London, U.K.
    244 Merton College, University of Oxford, OX1 4JD, Oxford, U.K.
    245 School of Physics, NanKai University, 300071, Tianjin, P.R. China
    246 rdf:type schema:Organization
    247 grid-institutes:grid.263901.f schema:alternateName School of Mathematics, Southwest Jiaotong University, West Zone, High-Tech District, 611756, Chengdu, Sichuan, China
    248 schema:name School of Mathematics, Southwest Jiaotong University, West Zone, High-Tech District, 611756, Chengdu, Sichuan, China
    249 rdf:type schema:Organization
    250 grid-institutes:grid.4991.5 schema:alternateName Pembroke College, University of Oxford, OX1 1DW, Oxford, U.K.
    251 schema:name Pembroke College, University of Oxford, OX1 1DW, Oxford, U.K.
    252 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...