Tρσ(G) theories and their Hilbert series View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-01-29

AUTHORS

Stefano Cremonesi, Amihay Hanany, Noppadol Mekareeya, Alberto Zaffaroni

ABSTRACT

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3dN=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} superconformal gauge theories Tρσ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups. More... »

PAGES

150

References to SciGraph publications

  • 2007-06-06. An Index for 4 Dimensional Super Conformal Theories in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2014-10-17. Down the rabbit hole with theories of class S in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-09-30. Coulomb branch Hilbert series and Hall-Littlewood polynomials in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-07-21. Describing codimension two defects in JOURNAL OF HIGH ENERGY PHYSICS
  • 1978-10. Polarizations in the classical groups in MATHEMATISCHE ZEITSCHRIFT
  • 2013-01-03. Bootstrapping the superconformal index with surface defects in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-08-19. Holographic duals of D = 3 superconformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-05-30. Exceptional indices in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-11-22. Mirror symmetry by O3-planes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-08-01. 3d partition function as overlap of wavefunctions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-12-06. Baryonic generating functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-06-20. Counting BPS baryonic operators in CFTs with Sasaki-Einstein duals in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-09-30. Coulomb branch Hilbert series and three dimensional Sicilian theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1982. Classes Unipotentes et Sous-groupes de Borel in NONE
  • 2012-09-19. Large N Free Energy of 3d = 4 SCFTs and AdS4/CFT3 in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-11-29. Counting chiral operators in quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-03. Monopole operators and Hilbert series of Coulomb branches of 3d\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} = 4 gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-09-16. Mirrors of 3d Sicilian theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-11-07. Gauge Theories and Macdonald Polynomials in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993-12. Line bundles on the cotangent bundle of the flag variety in INVENTIONES MATHEMATICAE
  • 1982-12. On the geometry of conjugacy classes in classical groups in COMMENTARII MATHEMATICI HELVETICI
  • 2010-01-21. Sicilian gauge theories and \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} = 1 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-10-21. Hanany-Witten effect and SL(2, ℤ) dualities in matrix models in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-06. An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient in TRANSFORMATION GROUPS
  • 2011-04-04. Index for three dimensional superconformal field theories with general R-charge assignments in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-06-10. Mirror symmetry in three dimensions via gauged linear quivers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-04-09. Sasaki–Einstein Manifolds and Volume Minimisation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-01. Symplectic resolutions for nilpotent orbits in INVENTIONES MATHEMATICAE
  • 2011-06-06. Superconformal indices of three-dimensional theories related by mirror symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep01(2015)150

    DOI

    http://dx.doi.org/10.1007/jhep01(2015)150

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1048031409


    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": "Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K.", 
              "id": "http://www.grid.ac/institutes/grid.7445.2", 
              "name": [
                "Department of Mathematics, King\u2019s College London, The Strand, WC2R 2LS, London, U.K.", 
                "Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Cremonesi", 
            "givenName": "Stefano", 
            "id": "sg:person.012634721705.50", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012634721705.50"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K.", 
              "id": "http://www.grid.ac/institutes/grid.7445.2", 
              "name": [
                "Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hanany", 
            "givenName": "Amihay", 
            "id": "sg:person.012155553275.80", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012155553275.80"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Theory Division, Physics Department, CERN, CH-1211, Geneva 23, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.9132.9", 
              "name": [
                "Theory Division, Physics Department, CERN, CH-1211, Geneva 23, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Mekareeya", 
            "givenName": "Noppadol", 
            "id": "sg:person.014662114762.32", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014662114762.32"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy", 
              "id": "http://www.grid.ac/institutes/grid.470207.6", 
              "name": [
                "Dipartimento di Fisica, Universit\u00e0 di Milano-Bicocca, I-20126, Milano, Italy", 
                "INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zaffaroni", 
            "givenName": "Alberto", 
            "id": "sg:person.010467526737.44", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010467526737.44"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/jhep07(2014)095", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048163068", 
              "https://doi.org/10.1007/jhep07(2014)095"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2000/11/033", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024992501", 
              "https://doi.org/10.1088/1126-6708/2000/11/033"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/06/069", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017451670", 
              "https://doi.org/10.1088/1126-6708/2007/06/069"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep10(2014)117", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003229445", 
              "https://doi.org/10.1007/jhep10(2014)117"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2014)059", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053069294", 
              "https://doi.org/10.1007/jhep06(2014)059"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2011)008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015999099", 
              "https://doi.org/10.1007/jhep06(2011)008"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep10(2014)099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019666118", 
              "https://doi.org/10.1007/jhep10(2014)099"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2011)087", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045833379", 
              "https://doi.org/10.1007/jhep08(2011)087"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2011)007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027488820", 
              "https://doi.org/10.1007/jhep04(2011)007"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2011)003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007953755", 
              "https://doi.org/10.1007/jhep08(2011)003"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00031-003-0422-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024875441", 
              "https://doi.org/10.1007/s00031-003-0422-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2013)022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030213861", 
              "https://doi.org/10.1007/jhep01(2013)022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/11/092", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022904471", 
              "https://doi.org/10.1088/1126-6708/2007/11/092"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01237035", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052704641", 
              "https://doi.org/10.1007/bf01237035"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01244299", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011196651", 
              "https://doi.org/10.1007/bf01244299"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2012)145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042516890", 
              "https://doi.org/10.1007/jhep05(2012)145"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2014)005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004476555", 
              "https://doi.org/10.1007/jhep01(2014)005"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-008-0479-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009921498", 
              "https://doi.org/10.1007/s00220-008-0479-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-007-0258-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040519445", 
              "https://doi.org/10.1007/s00220-007-0258-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2014)178", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052177898", 
              "https://doi.org/10.1007/jhep09(2014)178"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2010)063", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009424522", 
              "https://doi.org/10.1007/jhep09(2010)063"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/12/022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018393653", 
              "https://doi.org/10.1088/1126-6708/2007/12/022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02565876", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041235603", 
              "https://doi.org/10.1007/bf02565876"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0096302", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029540457", 
              "https://doi.org/10.1007/bfb0096302"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2012)074", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030981540", 
              "https://doi.org/10.1007/jhep09(2012)074"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-012-1607-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049095812", 
              "https://doi.org/10.1007/s00220-012-1607-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-002-0260-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050321688", 
              "https://doi.org/10.1007/s00222-002-0260-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)088", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032453331", 
              "https://doi.org/10.1007/jhep01(2010)088"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2014)185", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012825945", 
              "https://doi.org/10.1007/jhep09(2014)185"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2015-01-29", 
        "datePublishedReg": "2015-01-29", 
        "description": "We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3dN=4\\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}$$ \\mathcal{N}=4 $$\\end{document} superconformal gauge theories T\u03c1\u03c3(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, \u03c3 is a partition of G and \u03c1 a partition of the dual group G\u2228. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4\\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}$$ \\mathcal{N}=4 $$\\end{document} superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/jhep01(2015)150", 
        "isAccessibleForFree": true, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.3861842", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.2755951", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.3865945", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2015"
          }
        ], 
        "keywords": [
          "Hilbert series", 
          "Coulomb branch Hilbert series", 
          "superconformal gauge theories", 
          "Hall\u2013Littlewood polynomials", 
          "superconformal theories", 
          "mathematical language", 
          "gauge theory", 
          "D3-branes", 
          "classical groups", 
          "Coulomb branch", 
          "explicit formula", 
          "quantum Coulomb branch", 
          "case G", 
          "symplectic group", 
          "D5 branes", 
          "dual group", 
          "symmetric functions", 
          "theory", 
          "formula", 
          "interesting results", 
          "O3 plane", 
          "terms of localization", 
          "class", 
          "brane", 
          "polynomials", 
          "partition", 
          "generalization", 
          "terms", 
          "set", 
          "plane", 
          "Higgs", 
          "branches", 
          "results", 
          "function", 
          "series", 
          "use", 
          "localization", 
          "group", 
          "language", 
          "NS5"
        ], 
        "name": "T\u03c1\u03c3(G) theories and their Hilbert series", 
        "pagination": "150", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1048031409"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep01(2015)150"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep01(2015)150", 
          "https://app.dimensions.ai/details/publication/pub.1048031409"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-12-01T06:33", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_671.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/jhep01(2015)150"
      }
    ]
     

    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/jhep01(2015)150'

    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/jhep01(2015)150'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep01(2015)150'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep01(2015)150'


     

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

    248 TRIPLES      21 PREDICATES      93 URIs      56 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep01(2015)150 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N91075fe0c3a249ce9cea888c9d705ffb
    4 schema:citation sg:pub.10.1007/bf01237035
    5 sg:pub.10.1007/bf01244299
    6 sg:pub.10.1007/bf02565876
    7 sg:pub.10.1007/bfb0096302
    8 sg:pub.10.1007/jhep01(2010)088
    9 sg:pub.10.1007/jhep01(2013)022
    10 sg:pub.10.1007/jhep01(2014)005
    11 sg:pub.10.1007/jhep04(2011)007
    12 sg:pub.10.1007/jhep05(2012)145
    13 sg:pub.10.1007/jhep06(2011)008
    14 sg:pub.10.1007/jhep06(2014)059
    15 sg:pub.10.1007/jhep07(2014)095
    16 sg:pub.10.1007/jhep08(2011)003
    17 sg:pub.10.1007/jhep08(2011)087
    18 sg:pub.10.1007/jhep09(2010)063
    19 sg:pub.10.1007/jhep09(2012)074
    20 sg:pub.10.1007/jhep09(2014)178
    21 sg:pub.10.1007/jhep09(2014)185
    22 sg:pub.10.1007/jhep10(2014)099
    23 sg:pub.10.1007/jhep10(2014)117
    24 sg:pub.10.1007/s00031-003-0422-x
    25 sg:pub.10.1007/s00220-007-0258-7
    26 sg:pub.10.1007/s00220-008-0479-4
    27 sg:pub.10.1007/s00220-012-1607-8
    28 sg:pub.10.1007/s00222-002-0260-9
    29 sg:pub.10.1088/1126-6708/2000/11/033
    30 sg:pub.10.1088/1126-6708/2007/06/069
    31 sg:pub.10.1088/1126-6708/2007/11/092
    32 sg:pub.10.1088/1126-6708/2007/12/022
    33 schema:datePublished 2015-01-29
    34 schema:datePublishedReg 2015-01-29
    35 schema:description We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3dN=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} superconformal gauge theories Tρσ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups.
    36 schema:genre article
    37 schema:isAccessibleForFree true
    38 schema:isPartOf N2b6cc73cef22410482915055210710f2
    39 N36fe32bd579d42879f85e0c45b9e45ad
    40 sg:journal.1052482
    41 schema:keywords Coulomb branch
    42 Coulomb branch Hilbert series
    43 D3-branes
    44 D5 branes
    45 Hall–Littlewood polynomials
    46 Higgs
    47 Hilbert series
    48 NS5
    49 O3 plane
    50 branches
    51 brane
    52 case G
    53 class
    54 classical groups
    55 dual group
    56 explicit formula
    57 formula
    58 function
    59 gauge theory
    60 generalization
    61 group
    62 interesting results
    63 language
    64 localization
    65 mathematical language
    66 partition
    67 plane
    68 polynomials
    69 quantum Coulomb branch
    70 results
    71 series
    72 set
    73 superconformal gauge theories
    74 superconformal theories
    75 symmetric functions
    76 symplectic group
    77 terms
    78 terms of localization
    79 theory
    80 use
    81 schema:name Tρσ(G) theories and their Hilbert series
    82 schema:pagination 150
    83 schema:productId N83806a3148ff4aaaa10bc10139d0f872
    84 Nc25f7f7114dc4078b84c020808ea445d
    85 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048031409
    86 https://doi.org/10.1007/jhep01(2015)150
    87 schema:sdDatePublished 2022-12-01T06:33
    88 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    89 schema:sdPublisher N45bbfd83e58d438fbd3287492521f633
    90 schema:url https://doi.org/10.1007/jhep01(2015)150
    91 sgo:license sg:explorer/license/
    92 sgo:sdDataset articles
    93 rdf:type schema:ScholarlyArticle
    94 N1b310a46aa714f3e9fa0d143a8d6473c rdf:first sg:person.012155553275.80
    95 rdf:rest Ne9db3f79ed32421d96d2973e9f5d90f3
    96 N2b6cc73cef22410482915055210710f2 schema:issueNumber 1
    97 rdf:type schema:PublicationIssue
    98 N36fe32bd579d42879f85e0c45b9e45ad schema:volumeNumber 2015
    99 rdf:type schema:PublicationVolume
    100 N45bbfd83e58d438fbd3287492521f633 schema:name Springer Nature - SN SciGraph project
    101 rdf:type schema:Organization
    102 N83806a3148ff4aaaa10bc10139d0f872 schema:name dimensions_id
    103 schema:value pub.1048031409
    104 rdf:type schema:PropertyValue
    105 N91075fe0c3a249ce9cea888c9d705ffb rdf:first sg:person.012634721705.50
    106 rdf:rest N1b310a46aa714f3e9fa0d143a8d6473c
    107 Nc25f7f7114dc4078b84c020808ea445d schema:name doi
    108 schema:value 10.1007/jhep01(2015)150
    109 rdf:type schema:PropertyValue
    110 Nc99ee2bf2db24defbf0b5fd8473145cd rdf:first sg:person.010467526737.44
    111 rdf:rest rdf:nil
    112 Ne9db3f79ed32421d96d2973e9f5d90f3 rdf:first sg:person.014662114762.32
    113 rdf:rest Nc99ee2bf2db24defbf0b5fd8473145cd
    114 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    115 schema:name Mathematical Sciences
    116 rdf:type schema:DefinedTerm
    117 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    118 schema:name Pure Mathematics
    119 rdf:type schema:DefinedTerm
    120 sg:grant.2755951 http://pending.schema.org/fundedItem sg:pub.10.1007/jhep01(2015)150
    121 rdf:type schema:MonetaryGrant
    122 sg:grant.3861842 http://pending.schema.org/fundedItem sg:pub.10.1007/jhep01(2015)150
    123 rdf:type schema:MonetaryGrant
    124 sg:grant.3865945 http://pending.schema.org/fundedItem sg:pub.10.1007/jhep01(2015)150
    125 rdf:type schema:MonetaryGrant
    126 sg:journal.1052482 schema:issn 1029-8479
    127 1126-6708
    128 schema:name Journal of High Energy Physics
    129 schema:publisher Springer Nature
    130 rdf:type schema:Periodical
    131 sg:person.010467526737.44 schema:affiliation grid-institutes:grid.470207.6
    132 schema:familyName Zaffaroni
    133 schema:givenName Alberto
    134 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010467526737.44
    135 rdf:type schema:Person
    136 sg:person.012155553275.80 schema:affiliation grid-institutes:grid.7445.2
    137 schema:familyName Hanany
    138 schema:givenName Amihay
    139 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012155553275.80
    140 rdf:type schema:Person
    141 sg:person.012634721705.50 schema:affiliation grid-institutes:grid.7445.2
    142 schema:familyName Cremonesi
    143 schema:givenName Stefano
    144 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012634721705.50
    145 rdf:type schema:Person
    146 sg:person.014662114762.32 schema:affiliation grid-institutes:grid.9132.9
    147 schema:familyName Mekareeya
    148 schema:givenName Noppadol
    149 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014662114762.32
    150 rdf:type schema:Person
    151 sg:pub.10.1007/bf01237035 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052704641
    152 https://doi.org/10.1007/bf01237035
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1007/bf01244299 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011196651
    155 https://doi.org/10.1007/bf01244299
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/bf02565876 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041235603
    158 https://doi.org/10.1007/bf02565876
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/bfb0096302 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029540457
    161 https://doi.org/10.1007/bfb0096302
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1007/jhep01(2010)088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032453331
    164 https://doi.org/10.1007/jhep01(2010)088
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1007/jhep01(2013)022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030213861
    167 https://doi.org/10.1007/jhep01(2013)022
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/jhep01(2014)005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004476555
    170 https://doi.org/10.1007/jhep01(2014)005
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/jhep04(2011)007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027488820
    173 https://doi.org/10.1007/jhep04(2011)007
    174 rdf:type schema:CreativeWork
    175 sg:pub.10.1007/jhep05(2012)145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042516890
    176 https://doi.org/10.1007/jhep05(2012)145
    177 rdf:type schema:CreativeWork
    178 sg:pub.10.1007/jhep06(2011)008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015999099
    179 https://doi.org/10.1007/jhep06(2011)008
    180 rdf:type schema:CreativeWork
    181 sg:pub.10.1007/jhep06(2014)059 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053069294
    182 https://doi.org/10.1007/jhep06(2014)059
    183 rdf:type schema:CreativeWork
    184 sg:pub.10.1007/jhep07(2014)095 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048163068
    185 https://doi.org/10.1007/jhep07(2014)095
    186 rdf:type schema:CreativeWork
    187 sg:pub.10.1007/jhep08(2011)003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007953755
    188 https://doi.org/10.1007/jhep08(2011)003
    189 rdf:type schema:CreativeWork
    190 sg:pub.10.1007/jhep08(2011)087 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045833379
    191 https://doi.org/10.1007/jhep08(2011)087
    192 rdf:type schema:CreativeWork
    193 sg:pub.10.1007/jhep09(2010)063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009424522
    194 https://doi.org/10.1007/jhep09(2010)063
    195 rdf:type schema:CreativeWork
    196 sg:pub.10.1007/jhep09(2012)074 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030981540
    197 https://doi.org/10.1007/jhep09(2012)074
    198 rdf:type schema:CreativeWork
    199 sg:pub.10.1007/jhep09(2014)178 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052177898
    200 https://doi.org/10.1007/jhep09(2014)178
    201 rdf:type schema:CreativeWork
    202 sg:pub.10.1007/jhep09(2014)185 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012825945
    203 https://doi.org/10.1007/jhep09(2014)185
    204 rdf:type schema:CreativeWork
    205 sg:pub.10.1007/jhep10(2014)099 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019666118
    206 https://doi.org/10.1007/jhep10(2014)099
    207 rdf:type schema:CreativeWork
    208 sg:pub.10.1007/jhep10(2014)117 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003229445
    209 https://doi.org/10.1007/jhep10(2014)117
    210 rdf:type schema:CreativeWork
    211 sg:pub.10.1007/s00031-003-0422-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1024875441
    212 https://doi.org/10.1007/s00031-003-0422-x
    213 rdf:type schema:CreativeWork
    214 sg:pub.10.1007/s00220-007-0258-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040519445
    215 https://doi.org/10.1007/s00220-007-0258-7
    216 rdf:type schema:CreativeWork
    217 sg:pub.10.1007/s00220-008-0479-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009921498
    218 https://doi.org/10.1007/s00220-008-0479-4
    219 rdf:type schema:CreativeWork
    220 sg:pub.10.1007/s00220-012-1607-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049095812
    221 https://doi.org/10.1007/s00220-012-1607-8
    222 rdf:type schema:CreativeWork
    223 sg:pub.10.1007/s00222-002-0260-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050321688
    224 https://doi.org/10.1007/s00222-002-0260-9
    225 rdf:type schema:CreativeWork
    226 sg:pub.10.1088/1126-6708/2000/11/033 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024992501
    227 https://doi.org/10.1088/1126-6708/2000/11/033
    228 rdf:type schema:CreativeWork
    229 sg:pub.10.1088/1126-6708/2007/06/069 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017451670
    230 https://doi.org/10.1088/1126-6708/2007/06/069
    231 rdf:type schema:CreativeWork
    232 sg:pub.10.1088/1126-6708/2007/11/092 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022904471
    233 https://doi.org/10.1088/1126-6708/2007/11/092
    234 rdf:type schema:CreativeWork
    235 sg:pub.10.1088/1126-6708/2007/12/022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018393653
    236 https://doi.org/10.1088/1126-6708/2007/12/022
    237 rdf:type schema:CreativeWork
    238 grid-institutes:grid.470207.6 schema:alternateName INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy
    239 schema:name Dipartimento di Fisica, Università di Milano-Bicocca, I-20126, Milano, Italy
    240 INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy
    241 rdf:type schema:Organization
    242 grid-institutes:grid.7445.2 schema:alternateName Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K.
    243 schema:name Department of Mathematics, King’s College London, The Strand, WC2R 2LS, London, U.K.
    244 Theoretical Physics Group, Imperial College London, Prince Consort Road, SW7 2AZ, London, U.K.
    245 rdf:type schema:Organization
    246 grid-institutes:grid.9132.9 schema:alternateName Theory Division, Physics Department, CERN, CH-1211, Geneva 23, Switzerland
    247 schema:name Theory Division, Physics Department, CERN, CH-1211, Geneva 23, Switzerland
    248 rdf:type schema:Organization
     




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


    ...