A topologically twisted index for three-dimensional supersymmetric theories View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-07-23

AUTHORS

Francesco Benini, Alberto Zaffaroni

ABSTRACT

We provide a general formula for the partition function of three-dimensional N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} gauge theories placed on S2 ×S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 × T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants. More... »

PAGES

127

References to SciGraph publications

  • 1989-09. Quantum field theory and the Jones polynomial in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2012-08-10. Supersymmetry on curved spaces and holography in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-08-11. Higgs branch localization of N = 1 theories on S3 × S1 in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-03-17. 2d index and surface operators in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-11-29. Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03-08. S-duality and 2d topological QFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-10-17. Comments on 3d Seiberg-like dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-12-01. Toric reduction and a conjecture of Batyrev and Materov in INVENTIONES MATHEMATICAE
  • 2014-07-16. Comments on N = (2, 2) supersymmetry on two-manifolds in JOURNAL OF HIGH ENERGY PHYSICS
  • 1997. Conformal Field Theory in NONE
  • 2013-05-06. Supersymmetric field theories on three-manifolds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-05-08. Higgs branch localization in three dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-05-13. tt* geometry in 3 and 4 dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-06-12. The equivariant A-twist and gauged linear sigma models on the two-sphere in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-04-12. Static supersymmetric black holes in AdS4 with spherical symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-05-03. SUSY gauge theories on squashed three-spheres in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-09-21. Comments on Chern-Simons contact terms in three dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-12-22. Generalized indices for N = 1 theories in four-dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-05-14. Supersymmetry on three-dimensional Lorentzian curved spaces and black hole holography in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-23. The geometry of supersymmetric partition functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03-17. Exact results for Wilson loops in superconformal Chern-Simons theories with matter in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-12-30. Holomorphic blocks in three dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-06-01. Four-dimensional SCFTs from M5-branes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-08-06. N = 2 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-05-17. Exact results in D = 2 supersymmetric gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-07-17. Partition Functions of N=(2,2) Gauge Theories on S2 and Vortices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2012-05-22. Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2012-04-24. Factorisation of theories on the squashed 3-sphere in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-21. Supersymmetric AdS4 black holes and attractors in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-09. Webs of five-branes and 𝒩 = 2 superconformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-04-03. Exact Kähler potential from gauge theory and mirror symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-03-08. Flow equations and attractors for black holes in U(1) gauged supergravity in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-12-29. Non-Birational Twisted Derived Equivalences in Abelian GLSMs in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 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
  • 2014-11-02. Elliptic Genera of 2d N = 2 Gauge Theories in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-01-22. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2011-04-04. Index for three dimensional superconformal field theories with general R-charge assignments in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-12. Two-Sphere Partition Functions and Gromov–Witten Invariants in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-07-13. General instanton counting and 5d SCFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-11-30. Elliptic Genera of Two-Dimensional N=2 Gauge Theories with Rank-One Gauge Groups in LETTERS IN MATHEMATICAL PHYSICS
  • 2014-03-07. The = 1 Chiral Multiplet on T2 × S2 and Supersymmetric Localization in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-12-15. Gauge Theories Labelled by Three-Manifolds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-01-23. Witten index and wall crossing in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-05-25. Aspects of non-abelian gauge dynamics in two-dimensional 𝒩 = (2,2) theories in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep07(2015)127

    DOI

    http://dx.doi.org/10.1007/jhep07(2015)127

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1010821432


    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": "Blackett Laboratory, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom", 
              "id": "http://www.grid.ac/institutes/grid.7445.2", 
              "name": [
                "Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands", 
                "Blackett Laboratory, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Benini", 
            "givenName": "Francesco", 
            "id": "sg:person.011505670225.30", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011505670225.30"
            ], 
            "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/jhep12(2014)177", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006121047", 
              "https://doi.org/10.1007/jhep12(2014)177"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2012)005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001669470", 
              "https://doi.org/10.1007/jhep06(2012)005"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2013)093", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004670263", 
              "https://doi.org/10.1007/jhep05(2013)093"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2014)124", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049488438", 
              "https://doi.org/10.1007/jhep01(2014)124"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-014-2112-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007928508", 
              "https://doi.org/10.1007/s00220-014-2112-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-014-2210-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037293419", 
              "https://doi.org/10.1007/s00220-014-2210-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2011)037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039842659", 
              "https://doi.org/10.1007/jhep03(2011)037"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01217730", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033035951", 
              "https://doi.org/10.1007/bf01217730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)085", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026832128", 
              "https://doi.org/10.1007/jhep01(2010)085"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2011)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003742519", 
              "https://doi.org/10.1007/jhep05(2011)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2013)019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008614088", 
              "https://doi.org/10.1007/jhep04(2013)019"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2013)057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036843352", 
              "https://doi.org/10.1007/jhep05(2013)057"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep12(2014)150", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047807623", 
              "https://doi.org/10.1007/jhep12(2014)150"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)089", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052358077", 
              "https://doi.org/10.1007/jhep03(2010)089"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep10(2011)075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000059597", 
              "https://doi.org/10.1007/jhep10(2011)075"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2012)091", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019300516", 
              "https://doi.org/10.1007/jhep09(2012)091"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-004-0375-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008524964", 
              "https://doi.org/10.1007/s00222-004-0375-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-013-0673-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045565737", 
              "https://doi.org/10.1007/s11005-013-0673-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-013-1863-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039558900", 
              "https://doi.org/10.1007/s00220-013-1863-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-012-1485-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029100231", 
              "https://doi.org/10.1007/s00220-012-1485-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-2256-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016316421", 
              "https://doi.org/10.1007/978-1-4612-2256-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2012)061", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017854591", 
              "https://doi.org/10.1007/jhep08(2012)061"
            ], 
            "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.10.1007/jhep05(2014)030", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006312366", 
              "https://doi.org/10.1007/jhep05(2014)030"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2014)040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032698875", 
              "https://doi.org/10.1007/jhep03(2014)040"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-013-1874-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014849050", 
              "https://doi.org/10.1007/s00220-013-1874-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-009-0974-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035717698", 
              "https://doi.org/10.1007/s00220-009-0974-2"
            ], 
            "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.10.1088/1126-6708/2009/09/052", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004902104", 
              "https://doi.org/10.1088/1126-6708/2009/09/052"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2012)166", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000065736", 
              "https://doi.org/10.1007/jhep11(2012)166"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2014)055", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033565502", 
              "https://doi.org/10.1007/jhep05(2014)055"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2014)080", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028765881", 
              "https://doi.org/10.1007/jhep03(2014)080"
            ], 
            "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/jhep06(2015)076", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021793370", 
              "https://doi.org/10.1007/jhep06(2015)076"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2011)047", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052928837", 
              "https://doi.org/10.1007/jhep04(2011)047"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025314613", 
              "https://doi.org/10.1007/jhep03(2010)032"
            ], 
            "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/jhep01(2015)124", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029253322", 
              "https://doi.org/10.1007/jhep01(2015)124"
            ], 
            "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/jhep07(2014)075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050704071", 
              "https://doi.org/10.1007/jhep07(2014)075"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2014)060", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052298413", 
              "https://doi.org/10.1007/jhep08(2014)060"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2012)120", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005055998", 
              "https://doi.org/10.1007/jhep04(2012)120"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2013)017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008976617", 
              "https://doi.org/10.1007/jhep05(2013)017"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/05/079", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005771754", 
              "https://doi.org/10.1088/1126-6708/2007/05/079"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2015-07-23", 
        "datePublishedReg": "2015-07-23", 
        "description": "We provide a general formula for the partition function of three-dimensional N=2\\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}$$ \\mathcal{N}=2 $$\\end{document} gauge theories placed on S2 \u00d7S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to \u03a9-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 \u00d7 T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/jhep07(2015)127", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "7", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2015"
          }
        ], 
        "keywords": [
          "magnetic flux", 
          "partition function", 
          "Chern-Simons theory", 
          "Gromov\u2013Witten invariants", 
          "background magnetic fluxes", 
          "background magnetic field", 
          "four-dimensional theory", 
          "two-dimensional theory", 
          "Giveon-Kutasov duality", 
          "meromorphic form", 
          "\u03a9-background", 
          "topological twist", 
          "global symmetry", 
          "gauge theory", 
          "Yang-Mills", 
          "twisted index", 
          "magnetic field", 
          "zero modes", 
          "\u00d7 T2", 
          "supersymmetric theories", 
          "topological amplitudes", 
          "chiral states", 
          "theory", 
          "formula", 
          "general formula", 
          "Aharony", 
          "invariants", 
          "duality", 
          "symmetry", 
          "function", 
          "flux", 
          "sum", 
          "field", 
          "amplitude", 
          "alternative way", 
          "twist", 
          "S2", 
          "state", 
          "form", 
          "results", 
          "way", 
          "matter", 
          "index", 
          "fugacity", 
          "T2", 
          "collection", 
          "residues", 
          "example"
        ], 
        "name": "A topologically twisted index for three-dimensional supersymmetric theories", 
        "pagination": "127", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1010821432"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep07(2015)127"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep07(2015)127", 
          "https://app.dimensions.ai/details/publication/pub.1010821432"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-12-01T06:32", 
        "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_647.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/jhep07(2015)127"
      }
    ]
     

    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/jhep07(2015)127'

    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/jhep07(2015)127'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep07(2015)127'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep07(2015)127'


     

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

    293 TRIPLES      21 PREDICATES      116 URIs      64 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep07(2015)127 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nedcfc08b1d1d431294fbbcd18a435711
    4 schema:citation sg:pub.10.1007/978-1-4612-2256-9
    5 sg:pub.10.1007/bf01217730
    6 sg:pub.10.1007/jhep01(2010)085
    7 sg:pub.10.1007/jhep01(2010)088
    8 sg:pub.10.1007/jhep01(2014)124
    9 sg:pub.10.1007/jhep01(2015)124
    10 sg:pub.10.1007/jhep03(2010)032
    11 sg:pub.10.1007/jhep03(2010)089
    12 sg:pub.10.1007/jhep03(2011)037
    13 sg:pub.10.1007/jhep03(2014)040
    14 sg:pub.10.1007/jhep03(2014)080
    15 sg:pub.10.1007/jhep04(2011)007
    16 sg:pub.10.1007/jhep04(2011)047
    17 sg:pub.10.1007/jhep04(2012)120
    18 sg:pub.10.1007/jhep04(2013)019
    19 sg:pub.10.1007/jhep05(2011)014
    20 sg:pub.10.1007/jhep05(2013)017
    21 sg:pub.10.1007/jhep05(2013)057
    22 sg:pub.10.1007/jhep05(2013)093
    23 sg:pub.10.1007/jhep05(2014)030
    24 sg:pub.10.1007/jhep05(2014)055
    25 sg:pub.10.1007/jhep06(2012)005
    26 sg:pub.10.1007/jhep06(2015)076
    27 sg:pub.10.1007/jhep07(2014)075
    28 sg:pub.10.1007/jhep07(2015)063
    29 sg:pub.10.1007/jhep08(2012)034
    30 sg:pub.10.1007/jhep08(2012)061
    31 sg:pub.10.1007/jhep08(2014)060
    32 sg:pub.10.1007/jhep09(2012)091
    33 sg:pub.10.1007/jhep10(2011)075
    34 sg:pub.10.1007/jhep11(2012)166
    35 sg:pub.10.1007/jhep12(2014)150
    36 sg:pub.10.1007/jhep12(2014)177
    37 sg:pub.10.1007/s00220-009-0974-2
    38 sg:pub.10.1007/s00220-012-1485-0
    39 sg:pub.10.1007/s00220-013-1863-2
    40 sg:pub.10.1007/s00220-013-1874-z
    41 sg:pub.10.1007/s00220-014-2112-z
    42 sg:pub.10.1007/s00220-014-2210-y
    43 sg:pub.10.1007/s00222-004-0375-2
    44 sg:pub.10.1007/s11005-010-0369-5
    45 sg:pub.10.1007/s11005-013-0673-y
    46 sg:pub.10.1088/1126-6708/2007/05/079
    47 sg:pub.10.1088/1126-6708/2009/09/052
    48 schema:datePublished 2015-07-23
    49 schema:datePublishedReg 2015-07-23
    50 schema:description We provide a general formula for the partition function of three-dimensional N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} gauge theories placed on S2 ×S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 × T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.
    51 schema:genre article
    52 schema:isAccessibleForFree true
    53 schema:isPartOf N5aed1177565c4ff0a8834c1ee8722ced
    54 Nc19dcda1f46a4fc0b6fc2d28074bbf4a
    55 sg:journal.1052482
    56 schema:keywords Aharony
    57 Chern-Simons theory
    58 Giveon-Kutasov duality
    59 Gromov–Witten invariants
    60 S2
    61 T2
    62 Yang-Mills
    63 alternative way
    64 amplitude
    65 background magnetic field
    66 background magnetic fluxes
    67 chiral states
    68 collection
    69 duality
    70 example
    71 field
    72 flux
    73 form
    74 formula
    75 four-dimensional theory
    76 fugacity
    77 function
    78 gauge theory
    79 general formula
    80 global symmetry
    81 index
    82 invariants
    83 magnetic field
    84 magnetic flux
    85 matter
    86 meromorphic form
    87 partition function
    88 residues
    89 results
    90 state
    91 sum
    92 supersymmetric theories
    93 symmetry
    94 theory
    95 topological amplitudes
    96 topological twist
    97 twist
    98 twisted index
    99 two-dimensional theory
    100 way
    101 zero modes
    102 × T2
    103 Ω-background
    104 schema:name A topologically twisted index for three-dimensional supersymmetric theories
    105 schema:pagination 127
    106 schema:productId N37de4ff495b748069872019e239cd5a8
    107 N84041b760b184312aa491df96a229c56
    108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010821432
    109 https://doi.org/10.1007/jhep07(2015)127
    110 schema:sdDatePublished 2022-12-01T06:32
    111 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    112 schema:sdPublisher Nc134863cf89f4bd79c4ad7fada31e41b
    113 schema:url https://doi.org/10.1007/jhep07(2015)127
    114 sgo:license sg:explorer/license/
    115 sgo:sdDataset articles
    116 rdf:type schema:ScholarlyArticle
    117 N37de4ff495b748069872019e239cd5a8 schema:name dimensions_id
    118 schema:value pub.1010821432
    119 rdf:type schema:PropertyValue
    120 N550730808bde4da4ae7edebe5f9194ca rdf:first sg:person.010467526737.44
    121 rdf:rest rdf:nil
    122 N5aed1177565c4ff0a8834c1ee8722ced schema:volumeNumber 2015
    123 rdf:type schema:PublicationVolume
    124 N84041b760b184312aa491df96a229c56 schema:name doi
    125 schema:value 10.1007/jhep07(2015)127
    126 rdf:type schema:PropertyValue
    127 Nc134863cf89f4bd79c4ad7fada31e41b schema:name Springer Nature - SN SciGraph project
    128 rdf:type schema:Organization
    129 Nc19dcda1f46a4fc0b6fc2d28074bbf4a schema:issueNumber 7
    130 rdf:type schema:PublicationIssue
    131 Nedcfc08b1d1d431294fbbcd18a435711 rdf:first sg:person.011505670225.30
    132 rdf:rest N550730808bde4da4ae7edebe5f9194ca
    133 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    134 schema:name Mathematical Sciences
    135 rdf:type schema:DefinedTerm
    136 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    137 schema:name Pure Mathematics
    138 rdf:type schema:DefinedTerm
    139 sg:journal.1052482 schema:issn 1029-8479
    140 1126-6708
    141 schema:name Journal of High Energy Physics
    142 schema:publisher Springer Nature
    143 rdf:type schema:Periodical
    144 sg:person.010467526737.44 schema:affiliation grid-institutes:grid.470207.6
    145 schema:familyName Zaffaroni
    146 schema:givenName Alberto
    147 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010467526737.44
    148 rdf:type schema:Person
    149 sg:person.011505670225.30 schema:affiliation grid-institutes:grid.7445.2
    150 schema:familyName Benini
    151 schema:givenName Francesco
    152 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011505670225.30
    153 rdf:type schema:Person
    154 sg:pub.10.1007/978-1-4612-2256-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016316421
    155 https://doi.org/10.1007/978-1-4612-2256-9
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/bf01217730 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033035951
    158 https://doi.org/10.1007/bf01217730
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/jhep01(2010)085 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026832128
    161 https://doi.org/10.1007/jhep01(2010)085
    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(2014)124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049488438
    167 https://doi.org/10.1007/jhep01(2014)124
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/jhep01(2015)124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029253322
    170 https://doi.org/10.1007/jhep01(2015)124
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/jhep03(2010)032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025314613
    173 https://doi.org/10.1007/jhep03(2010)032
    174 rdf:type schema:CreativeWork
    175 sg:pub.10.1007/jhep03(2010)089 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052358077
    176 https://doi.org/10.1007/jhep03(2010)089
    177 rdf:type schema:CreativeWork
    178 sg:pub.10.1007/jhep03(2011)037 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039842659
    179 https://doi.org/10.1007/jhep03(2011)037
    180 rdf:type schema:CreativeWork
    181 sg:pub.10.1007/jhep03(2014)040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032698875
    182 https://doi.org/10.1007/jhep03(2014)040
    183 rdf:type schema:CreativeWork
    184 sg:pub.10.1007/jhep03(2014)080 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028765881
    185 https://doi.org/10.1007/jhep03(2014)080
    186 rdf:type schema:CreativeWork
    187 sg:pub.10.1007/jhep04(2011)007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027488820
    188 https://doi.org/10.1007/jhep04(2011)007
    189 rdf:type schema:CreativeWork
    190 sg:pub.10.1007/jhep04(2011)047 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052928837
    191 https://doi.org/10.1007/jhep04(2011)047
    192 rdf:type schema:CreativeWork
    193 sg:pub.10.1007/jhep04(2012)120 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005055998
    194 https://doi.org/10.1007/jhep04(2012)120
    195 rdf:type schema:CreativeWork
    196 sg:pub.10.1007/jhep04(2013)019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008614088
    197 https://doi.org/10.1007/jhep04(2013)019
    198 rdf:type schema:CreativeWork
    199 sg:pub.10.1007/jhep05(2011)014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003742519
    200 https://doi.org/10.1007/jhep05(2011)014
    201 rdf:type schema:CreativeWork
    202 sg:pub.10.1007/jhep05(2013)017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008976617
    203 https://doi.org/10.1007/jhep05(2013)017
    204 rdf:type schema:CreativeWork
    205 sg:pub.10.1007/jhep05(2013)057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036843352
    206 https://doi.org/10.1007/jhep05(2013)057
    207 rdf:type schema:CreativeWork
    208 sg:pub.10.1007/jhep05(2013)093 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004670263
    209 https://doi.org/10.1007/jhep05(2013)093
    210 rdf:type schema:CreativeWork
    211 sg:pub.10.1007/jhep05(2014)030 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006312366
    212 https://doi.org/10.1007/jhep05(2014)030
    213 rdf:type schema:CreativeWork
    214 sg:pub.10.1007/jhep05(2014)055 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033565502
    215 https://doi.org/10.1007/jhep05(2014)055
    216 rdf:type schema:CreativeWork
    217 sg:pub.10.1007/jhep06(2012)005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001669470
    218 https://doi.org/10.1007/jhep06(2012)005
    219 rdf:type schema:CreativeWork
    220 sg:pub.10.1007/jhep06(2015)076 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021793370
    221 https://doi.org/10.1007/jhep06(2015)076
    222 rdf:type schema:CreativeWork
    223 sg:pub.10.1007/jhep07(2014)075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050704071
    224 https://doi.org/10.1007/jhep07(2014)075
    225 rdf:type schema:CreativeWork
    226 sg:pub.10.1007/jhep07(2015)063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016122204
    227 https://doi.org/10.1007/jhep07(2015)063
    228 rdf:type schema:CreativeWork
    229 sg:pub.10.1007/jhep08(2012)034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000072911
    230 https://doi.org/10.1007/jhep08(2012)034
    231 rdf:type schema:CreativeWork
    232 sg:pub.10.1007/jhep08(2012)061 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017854591
    233 https://doi.org/10.1007/jhep08(2012)061
    234 rdf:type schema:CreativeWork
    235 sg:pub.10.1007/jhep08(2014)060 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052298413
    236 https://doi.org/10.1007/jhep08(2014)060
    237 rdf:type schema:CreativeWork
    238 sg:pub.10.1007/jhep09(2012)091 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019300516
    239 https://doi.org/10.1007/jhep09(2012)091
    240 rdf:type schema:CreativeWork
    241 sg:pub.10.1007/jhep10(2011)075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000059597
    242 https://doi.org/10.1007/jhep10(2011)075
    243 rdf:type schema:CreativeWork
    244 sg:pub.10.1007/jhep11(2012)166 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000065736
    245 https://doi.org/10.1007/jhep11(2012)166
    246 rdf:type schema:CreativeWork
    247 sg:pub.10.1007/jhep12(2014)150 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047807623
    248 https://doi.org/10.1007/jhep12(2014)150
    249 rdf:type schema:CreativeWork
    250 sg:pub.10.1007/jhep12(2014)177 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006121047
    251 https://doi.org/10.1007/jhep12(2014)177
    252 rdf:type schema:CreativeWork
    253 sg:pub.10.1007/s00220-009-0974-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035717698
    254 https://doi.org/10.1007/s00220-009-0974-2
    255 rdf:type schema:CreativeWork
    256 sg:pub.10.1007/s00220-012-1485-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029100231
    257 https://doi.org/10.1007/s00220-012-1485-0
    258 rdf:type schema:CreativeWork
    259 sg:pub.10.1007/s00220-013-1863-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039558900
    260 https://doi.org/10.1007/s00220-013-1863-2
    261 rdf:type schema:CreativeWork
    262 sg:pub.10.1007/s00220-013-1874-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1014849050
    263 https://doi.org/10.1007/s00220-013-1874-z
    264 rdf:type schema:CreativeWork
    265 sg:pub.10.1007/s00220-014-2112-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1007928508
    266 https://doi.org/10.1007/s00220-014-2112-z
    267 rdf:type schema:CreativeWork
    268 sg:pub.10.1007/s00220-014-2210-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1037293419
    269 https://doi.org/10.1007/s00220-014-2210-y
    270 rdf:type schema:CreativeWork
    271 sg:pub.10.1007/s00222-004-0375-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008524964
    272 https://doi.org/10.1007/s00222-004-0375-2
    273 rdf:type schema:CreativeWork
    274 sg:pub.10.1007/s11005-010-0369-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022882223
    275 https://doi.org/10.1007/s11005-010-0369-5
    276 rdf:type schema:CreativeWork
    277 sg:pub.10.1007/s11005-013-0673-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1045565737
    278 https://doi.org/10.1007/s11005-013-0673-y
    279 rdf:type schema:CreativeWork
    280 sg:pub.10.1088/1126-6708/2007/05/079 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005771754
    281 https://doi.org/10.1088/1126-6708/2007/05/079
    282 rdf:type schema:CreativeWork
    283 sg:pub.10.1088/1126-6708/2009/09/052 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004902104
    284 https://doi.org/10.1088/1126-6708/2009/09/052
    285 rdf:type schema:CreativeWork
    286 grid-institutes:grid.470207.6 schema:alternateName INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy
    287 schema:name Dipartimento di Fisica, Università di Milano-Bicocca, I-20126, Milano, Italy
    288 INFN, sezione di Milano-Bicocca, I-20126, Milano, Italy
    289 rdf:type schema:Organization
    290 grid-institutes:grid.7445.2 schema:alternateName Blackett Laboratory, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom
    291 schema:name Blackett Laboratory, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom
    292 Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands
    293 rdf:type schema:Organization
     




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


    ...