Multiple D3-Instantons and Mock Modular Forms I View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-07

AUTHORS

Sergei Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline

ABSTRACT

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi–Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson–Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson–Thomas invariants of pure two-dimensional sheaves. More... »

PAGES

379-411

References to SciGraph publications

  • 2009-03-06. D-instantons and twistors in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012. Quantum Black Holes in STRINGS AND FUNDAMENTAL PHYSICS
  • 2007-05-29. Quantum covariant c-map in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-11-17. Black hole bound states in AdS3 × S2 in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-06. The non-compact elliptic genus: mock or modular in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-11. Dualities and fivebrane instantons in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-08-30. Supergravity flows and D-brane stability in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-11-10. A Farey tail for attractor black holes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-02. Calabi–Yau Black Holes and (0,4) Sigma Models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-09-25. Quantum mirror symmetry and twistors in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-04. D3-instantons, mock theta series and twistors in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-08. S-duality in twistor space in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-03-27. String loop corrected hypermultiplet moduli spaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 1977. Séries thêta des formes quadratiques indéfinies in MODULAR FUNCTIONS OF ONE VARIABLE VI
  • 1997-12-07. Black hole entropy in M-Theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-06. Linear Perturbations of Quaternionic Metrics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-08-24. The M5-brane elliptic genus: modularity and BPS states in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-11. Wall-Crossing Holomorphic Anomaly and Mock Modularity of Multiple M5-Branes in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-04. Wall-crossing made smooth in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-03. Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 2017-03. Vertical D4–D2–D0 Bound States on K3 Fibrations and Modularity in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-10. Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-11. Stability and Duality in \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} Supergravity in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2011-07. Wall crossing from Boltzmann black hole halos in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-11-05. Examples of M5-brane elliptic genera in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-12. Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-11. Split states, entropy enigmas, holes and halos in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-016-2799-0

    DOI

    http://dx.doi.org/10.1007/s00220-016-2799-0

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1020836646


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Laboratoire Charles Coulomb", 
              "id": "https://www.grid.ac/institutes/grid.462669.9", 
              "name": [
                "Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Universit\u00e9 de Montpellier, 34095, Montpellier, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Alexandrov", 
            "givenName": "Sergei", 
            "id": "sg:person.013353510521.51", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013353510521.51"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "L'Institut de physique th\u00e9orique", 
              "id": "https://www.grid.ac/institutes/grid.457338.e", 
              "name": [
                "IPhT, CEA, Saclay, 91191, Gif-sur-Yvette, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Banerjee", 
            "givenName": "Sibasish", 
            "id": "sg:person.07410672327.38", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07410672327.38"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Trinity College Dublin", 
              "id": "https://www.grid.ac/institutes/grid.8217.c", 
              "name": [
                "School of Mathematics, Trinity College, Dublin 2, Ireland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Manschot", 
            "givenName": "Jan", 
            "id": "sg:person.015717054723.85", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015717054723.85"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Laboratory of Theoretical and High Energy Physics", 
              "id": "https://www.grid.ac/institutes/grid.463942.e", 
              "name": [
                "CERN PH-TH, Case C01600, CERN, 1211, Geneva 23, Switzerland", 
                "Laboratoire de Physique Th\u00e9orique et Hautes Energies, CNRS UMR 7589, Universit\u00e9 Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pioline", 
            "givenName": "Boris", 
            "id": "sg:person.015100720111.21", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015100720111.21"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/jhep11(2011)129", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001096026", 
              "https://doi.org/10.1007/jhep11(2011)129"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-016-2772-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001735938", 
              "https://doi.org/10.1007/s00220-016-2772-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-016-2772-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001735938", 
              "https://doi.org/10.1007/s00220-016-2772-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.52.r5412", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001776675"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.52.r5412", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001776675"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-25947-0_5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002849447", 
              "https://doi.org/10.1007/978-3-642-25947-0_5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(83)90605-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003710071"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(83)90605-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003710071"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2014)040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007441399", 
              "https://doi.org/10.1007/jhep11(2014)040"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2015)092", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010393057", 
              "https://doi.org/10.1007/jhep04(2015)092"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2015)092", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010393057", 
              "https://doi.org/10.1007/jhep04(2015)092"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(93)90548-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010912730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(93)90548-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010912730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90097-w", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014073937"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90097-w", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014073937"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2011)059", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016776190", 
              "https://doi.org/10.1007/jhep07(2011)059"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-015-2436-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016818205", 
              "https://doi.org/10.1007/s00220-015-2436-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/1751-8113/42/33/335402", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016995997"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/1751-8113/42/33/335402", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016995997"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/08/070", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018895875", 
              "https://doi.org/10.1088/1126-6708/2007/08/070"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.4826603", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019911938"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1353/ajm.2013.0031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019918015"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physrep.2012.09.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020696807"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/20/23/009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021753822"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/11/024", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023163883", 
              "https://doi.org/10.1088/1126-6708/2006/11/024"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.114.121601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023919274"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.114.121601", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023919274"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/03/044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024976024", 
              "https://doi.org/10.1088/1126-6708/2009/03/044"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/03/044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024976024", 
              "https://doi.org/10.1088/1126-6708/2009/03/044"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/03/081", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025695146", 
              "https://doi.org/10.1088/1126-6708/2006/03/081"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/03/081", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025695146", 
              "https://doi.org/10.1088/1126-6708/2006/03/081"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.90.041902", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026553148"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.90.041902", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026553148"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/1997/12/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028846542", 
              "https://doi.org/10.1088/1126-6708/1997/12/002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/05/094", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029060859", 
              "https://doi.org/10.1088/1126-6708/2007/05/094"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(99)00796-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030524649"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0065303", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030929487", 
              "https://doi.org/10.1007/bfb0065303"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(97)00572-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033708441"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1022-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033750352", 
              "https://doi.org/10.1007/s00220-010-1022-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1022-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033750352", 
              "https://doi.org/10.1007/s00220-010-1022-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2012)112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035177403", 
              "https://doi.org/10.1007/jhep08(2012)112"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/11/004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036441222", 
              "https://doi.org/10.1088/1126-6708/2007/11/004"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036528515", 
              "https://doi.org/10.1088/1126-6708/2009/09/108"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036528515", 
              "https://doi.org/10.1088/1126-6708/2009/09/108"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2008/11/050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039723749", 
              "https://doi.org/10.1088/1126-6708/2008/11/050"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)90097-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039866135"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)90097-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039866135"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1071-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040539415", 
              "https://doi.org/10.1007/s00220-010-1071-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1071-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040539415", 
              "https://doi.org/10.1007/s00220-010-1071-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2000/08/050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041124401", 
              "https://doi.org/10.1088/1126-6708/2000/08/050"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.98.211602", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042261907"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.98.211602", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042261907"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(98)00426-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042398666"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2013)002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044196315", 
              "https://doi.org/10.1007/jhep04(2013)002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00020960", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044524270", 
              "https://doi.org/10.1007/pl00020960"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/(sici)1521-3978(20001)48:1/3<119::aid-prop119>3.0.co;2-#", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044861867"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep12(2011)027", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049003284", 
              "https://doi.org/10.1007/jhep12(2011)027"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2011)111", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051216904", 
              "https://doi.org/10.1007/jhep03(2011)111"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2010)104", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053078320", 
              "https://doi.org/10.1007/jhep06(2010)104"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2010)104", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053078320", 
              "https://doi.org/10.1007/jhep06(2010)104"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1104-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053149442", 
              "https://doi.org/10.1007/s00220-010-1104-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-010-1104-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053149442", 
              "https://doi.org/10.1007/s00220-010-1104-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1374448", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057700303"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0065-9266-2011-00630-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059337554"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0129167x95000146", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062903453"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x89000972", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062928738"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/00127094-3129595", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064411471"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.2011.v15.n1.a1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072457321"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/cntp.2010.v4.n1.a3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072459478"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/cntp.2012.v6.n2.a4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072459517"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/cntp.2012.v6.n4.a5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072459526"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/jdg/1497405629", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1086017437"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/pspum/090/01523", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089187677"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1106891632", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/9781118032527", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1106891632"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2017-07", 
        "datePublishedReg": "2017-07-01", 
        "description": "We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi\u2013Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the K\u00e4hler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson\u2013Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson\u2013Thomas invariants of pure two-dimensional sheaves.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00220-016-2799-0", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "353"
          }
        ], 
        "name": "Multiple D3-Instantons and Mock Modular Forms I", 
        "pagination": "379-411", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "634758d1264b1eddf0defbad574840aca79534cdb68686c87d1a2095683f0cdf"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00220-016-2799-0"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1020836646"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00220-016-2799-0", 
          "https://app.dimensions.ai/details/publication/pub.1020836646"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T12:26", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000362_0000000362/records_87115_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00220-016-2799-0"
      }
    ]
     

    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/s00220-016-2799-0'

    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/s00220-016-2799-0'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-016-2799-0'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-016-2799-0'


     

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

    289 TRIPLES      21 PREDICATES      84 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00220-016-2799-0 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N9a920b0f0a57491880802141eace15a1
    4 schema:citation sg:pub.10.1007/978-3-642-25947-0_5
    5 sg:pub.10.1007/bfb0065303
    6 sg:pub.10.1007/jhep03(2011)111
    7 sg:pub.10.1007/jhep04(2013)002
    8 sg:pub.10.1007/jhep04(2015)092
    9 sg:pub.10.1007/jhep06(2010)104
    10 sg:pub.10.1007/jhep07(2011)059
    11 sg:pub.10.1007/jhep08(2012)112
    12 sg:pub.10.1007/jhep11(2011)129
    13 sg:pub.10.1007/jhep11(2014)040
    14 sg:pub.10.1007/jhep12(2011)027
    15 sg:pub.10.1007/pl00020960
    16 sg:pub.10.1007/s00220-010-1022-y
    17 sg:pub.10.1007/s00220-010-1071-2
    18 sg:pub.10.1007/s00220-010-1104-x
    19 sg:pub.10.1007/s00220-015-2436-3
    20 sg:pub.10.1007/s00220-016-2772-y
    21 sg:pub.10.1088/1126-6708/1997/12/002
    22 sg:pub.10.1088/1126-6708/2000/08/050
    23 sg:pub.10.1088/1126-6708/2006/03/081
    24 sg:pub.10.1088/1126-6708/2006/11/024
    25 sg:pub.10.1088/1126-6708/2007/05/094
    26 sg:pub.10.1088/1126-6708/2007/08/070
    27 sg:pub.10.1088/1126-6708/2007/11/004
    28 sg:pub.10.1088/1126-6708/2008/11/050
    29 sg:pub.10.1088/1126-6708/2009/03/044
    30 sg:pub.10.1088/1126-6708/2009/09/108
    31 https://app.dimensions.ai/details/publication/pub.1106891632
    32 https://doi.org/10.1002/(sici)1521-3978(20001)48:1/3<119::aid-prop119>3.0.co;2-#
    33 https://doi.org/10.1002/9781118032527
    34 https://doi.org/10.1016/0550-3213(83)90605-3
    35 https://doi.org/10.1016/0550-3213(90)90097-w
    36 https://doi.org/10.1016/0550-3213(93)90548-4
    37 https://doi.org/10.1016/0550-3213(94)90097-3
    38 https://doi.org/10.1016/j.physrep.2012.09.005
    39 https://doi.org/10.1016/s0550-3213(97)00572-5
    40 https://doi.org/10.1016/s0550-3213(98)00426-x
    41 https://doi.org/10.1016/s0550-3213(99)00796-8
    42 https://doi.org/10.1063/1.1374448
    43 https://doi.org/10.1063/1.4826603
    44 https://doi.org/10.1088/0264-9381/20/23/009
    45 https://doi.org/10.1088/1751-8113/42/33/335402
    46 https://doi.org/10.1090/pspum/090/01523
    47 https://doi.org/10.1090/s0065-9266-2011-00630-1
    48 https://doi.org/10.1103/physrevd.52.r5412
    49 https://doi.org/10.1103/physrevd.90.041902
    50 https://doi.org/10.1103/physrevlett.114.121601
    51 https://doi.org/10.1103/physrevlett.98.211602
    52 https://doi.org/10.1142/s0129167x95000146
    53 https://doi.org/10.1142/s0217751x89000972
    54 https://doi.org/10.1215/00127094-3129595
    55 https://doi.org/10.1353/ajm.2013.0031
    56 https://doi.org/10.4310/atmp.2011.v15.n1.a1
    57 https://doi.org/10.4310/cntp.2010.v4.n1.a3
    58 https://doi.org/10.4310/cntp.2012.v6.n2.a4
    59 https://doi.org/10.4310/cntp.2012.v6.n4.a5
    60 https://doi.org/10.4310/jdg/1497405629
    61 schema:datePublished 2017-07
    62 schema:datePublishedReg 2017-07-01
    63 schema:description We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi–Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson–Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson–Thomas invariants of pure two-dimensional sheaves.
    64 schema:genre research_article
    65 schema:inLanguage en
    66 schema:isAccessibleForFree true
    67 schema:isPartOf Na469e14d18f34513b2da60f2e949553f
    68 Nd7134bec493443d29f1feec2b8847b12
    69 sg:journal.1136216
    70 schema:name Multiple D3-Instantons and Mock Modular Forms I
    71 schema:pagination 379-411
    72 schema:productId N41f5cd27a5f54cdbb0cbc08fa187d8b5
    73 N49144fd867f145ef96ef67a1c166b8fc
    74 N573924407e54443aa611ab2f48a83e94
    75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020836646
    76 https://doi.org/10.1007/s00220-016-2799-0
    77 schema:sdDatePublished 2019-04-11T12:26
    78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    79 schema:sdPublisher N9caf2a1d13584492b2a738543f60130d
    80 schema:url https://link.springer.com/10.1007%2Fs00220-016-2799-0
    81 sgo:license sg:explorer/license/
    82 sgo:sdDataset articles
    83 rdf:type schema:ScholarlyArticle
    84 N41f5cd27a5f54cdbb0cbc08fa187d8b5 schema:name dimensions_id
    85 schema:value pub.1020836646
    86 rdf:type schema:PropertyValue
    87 N49144fd867f145ef96ef67a1c166b8fc schema:name readcube_id
    88 schema:value 634758d1264b1eddf0defbad574840aca79534cdb68686c87d1a2095683f0cdf
    89 rdf:type schema:PropertyValue
    90 N573924407e54443aa611ab2f48a83e94 schema:name doi
    91 schema:value 10.1007/s00220-016-2799-0
    92 rdf:type schema:PropertyValue
    93 N8936f2d01e4644be828552b3d4bbfe10 rdf:first sg:person.015100720111.21
    94 rdf:rest rdf:nil
    95 N9a920b0f0a57491880802141eace15a1 rdf:first sg:person.013353510521.51
    96 rdf:rest Nb5c84a9bb1ab4d10bf995be03fcc2e98
    97 N9caf2a1d13584492b2a738543f60130d schema:name Springer Nature - SN SciGraph project
    98 rdf:type schema:Organization
    99 Na469e14d18f34513b2da60f2e949553f schema:issueNumber 1
    100 rdf:type schema:PublicationIssue
    101 Nb137759b924f4353b07bf426cc15298e rdf:first sg:person.015717054723.85
    102 rdf:rest N8936f2d01e4644be828552b3d4bbfe10
    103 Nb5c84a9bb1ab4d10bf995be03fcc2e98 rdf:first sg:person.07410672327.38
    104 rdf:rest Nb137759b924f4353b07bf426cc15298e
    105 Nd7134bec493443d29f1feec2b8847b12 schema:volumeNumber 353
    106 rdf:type schema:PublicationVolume
    107 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    108 schema:name Mathematical Sciences
    109 rdf:type schema:DefinedTerm
    110 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    111 schema:name Pure Mathematics
    112 rdf:type schema:DefinedTerm
    113 sg:journal.1136216 schema:issn 0010-3616
    114 1432-0916
    115 schema:name Communications in Mathematical Physics
    116 rdf:type schema:Periodical
    117 sg:person.013353510521.51 schema:affiliation https://www.grid.ac/institutes/grid.462669.9
    118 schema:familyName Alexandrov
    119 schema:givenName Sergei
    120 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013353510521.51
    121 rdf:type schema:Person
    122 sg:person.015100720111.21 schema:affiliation https://www.grid.ac/institutes/grid.463942.e
    123 schema:familyName Pioline
    124 schema:givenName Boris
    125 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015100720111.21
    126 rdf:type schema:Person
    127 sg:person.015717054723.85 schema:affiliation https://www.grid.ac/institutes/grid.8217.c
    128 schema:familyName Manschot
    129 schema:givenName Jan
    130 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015717054723.85
    131 rdf:type schema:Person
    132 sg:person.07410672327.38 schema:affiliation https://www.grid.ac/institutes/grid.457338.e
    133 schema:familyName Banerjee
    134 schema:givenName Sibasish
    135 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07410672327.38
    136 rdf:type schema:Person
    137 sg:pub.10.1007/978-3-642-25947-0_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002849447
    138 https://doi.org/10.1007/978-3-642-25947-0_5
    139 rdf:type schema:CreativeWork
    140 sg:pub.10.1007/bfb0065303 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030929487
    141 https://doi.org/10.1007/bfb0065303
    142 rdf:type schema:CreativeWork
    143 sg:pub.10.1007/jhep03(2011)111 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051216904
    144 https://doi.org/10.1007/jhep03(2011)111
    145 rdf:type schema:CreativeWork
    146 sg:pub.10.1007/jhep04(2013)002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044196315
    147 https://doi.org/10.1007/jhep04(2013)002
    148 rdf:type schema:CreativeWork
    149 sg:pub.10.1007/jhep04(2015)092 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010393057
    150 https://doi.org/10.1007/jhep04(2015)092
    151 rdf:type schema:CreativeWork
    152 sg:pub.10.1007/jhep06(2010)104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053078320
    153 https://doi.org/10.1007/jhep06(2010)104
    154 rdf:type schema:CreativeWork
    155 sg:pub.10.1007/jhep07(2011)059 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016776190
    156 https://doi.org/10.1007/jhep07(2011)059
    157 rdf:type schema:CreativeWork
    158 sg:pub.10.1007/jhep08(2012)112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035177403
    159 https://doi.org/10.1007/jhep08(2012)112
    160 rdf:type schema:CreativeWork
    161 sg:pub.10.1007/jhep11(2011)129 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001096026
    162 https://doi.org/10.1007/jhep11(2011)129
    163 rdf:type schema:CreativeWork
    164 sg:pub.10.1007/jhep11(2014)040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007441399
    165 https://doi.org/10.1007/jhep11(2014)040
    166 rdf:type schema:CreativeWork
    167 sg:pub.10.1007/jhep12(2011)027 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049003284
    168 https://doi.org/10.1007/jhep12(2011)027
    169 rdf:type schema:CreativeWork
    170 sg:pub.10.1007/pl00020960 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044524270
    171 https://doi.org/10.1007/pl00020960
    172 rdf:type schema:CreativeWork
    173 sg:pub.10.1007/s00220-010-1022-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1033750352
    174 https://doi.org/10.1007/s00220-010-1022-y
    175 rdf:type schema:CreativeWork
    176 sg:pub.10.1007/s00220-010-1071-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040539415
    177 https://doi.org/10.1007/s00220-010-1071-2
    178 rdf:type schema:CreativeWork
    179 sg:pub.10.1007/s00220-010-1104-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1053149442
    180 https://doi.org/10.1007/s00220-010-1104-x
    181 rdf:type schema:CreativeWork
    182 sg:pub.10.1007/s00220-015-2436-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016818205
    183 https://doi.org/10.1007/s00220-015-2436-3
    184 rdf:type schema:CreativeWork
    185 sg:pub.10.1007/s00220-016-2772-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1001735938
    186 https://doi.org/10.1007/s00220-016-2772-y
    187 rdf:type schema:CreativeWork
    188 sg:pub.10.1088/1126-6708/1997/12/002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028846542
    189 https://doi.org/10.1088/1126-6708/1997/12/002
    190 rdf:type schema:CreativeWork
    191 sg:pub.10.1088/1126-6708/2000/08/050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041124401
    192 https://doi.org/10.1088/1126-6708/2000/08/050
    193 rdf:type schema:CreativeWork
    194 sg:pub.10.1088/1126-6708/2006/03/081 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025695146
    195 https://doi.org/10.1088/1126-6708/2006/03/081
    196 rdf:type schema:CreativeWork
    197 sg:pub.10.1088/1126-6708/2006/11/024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023163883
    198 https://doi.org/10.1088/1126-6708/2006/11/024
    199 rdf:type schema:CreativeWork
    200 sg:pub.10.1088/1126-6708/2007/05/094 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029060859
    201 https://doi.org/10.1088/1126-6708/2007/05/094
    202 rdf:type schema:CreativeWork
    203 sg:pub.10.1088/1126-6708/2007/08/070 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018895875
    204 https://doi.org/10.1088/1126-6708/2007/08/070
    205 rdf:type schema:CreativeWork
    206 sg:pub.10.1088/1126-6708/2007/11/004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036441222
    207 https://doi.org/10.1088/1126-6708/2007/11/004
    208 rdf:type schema:CreativeWork
    209 sg:pub.10.1088/1126-6708/2008/11/050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039723749
    210 https://doi.org/10.1088/1126-6708/2008/11/050
    211 rdf:type schema:CreativeWork
    212 sg:pub.10.1088/1126-6708/2009/03/044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024976024
    213 https://doi.org/10.1088/1126-6708/2009/03/044
    214 rdf:type schema:CreativeWork
    215 sg:pub.10.1088/1126-6708/2009/09/108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036528515
    216 https://doi.org/10.1088/1126-6708/2009/09/108
    217 rdf:type schema:CreativeWork
    218 https://app.dimensions.ai/details/publication/pub.1106891632 schema:CreativeWork
    219 https://doi.org/10.1002/(sici)1521-3978(20001)48:1/3<119::aid-prop119>3.0.co;2-# schema:sameAs https://app.dimensions.ai/details/publication/pub.1044861867
    220 rdf:type schema:CreativeWork
    221 https://doi.org/10.1002/9781118032527 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106891632
    222 rdf:type schema:CreativeWork
    223 https://doi.org/10.1016/0550-3213(83)90605-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003710071
    224 rdf:type schema:CreativeWork
    225 https://doi.org/10.1016/0550-3213(90)90097-w schema:sameAs https://app.dimensions.ai/details/publication/pub.1014073937
    226 rdf:type schema:CreativeWork
    227 https://doi.org/10.1016/0550-3213(93)90548-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010912730
    228 rdf:type schema:CreativeWork
    229 https://doi.org/10.1016/0550-3213(94)90097-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039866135
    230 rdf:type schema:CreativeWork
    231 https://doi.org/10.1016/j.physrep.2012.09.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020696807
    232 rdf:type schema:CreativeWork
    233 https://doi.org/10.1016/s0550-3213(97)00572-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033708441
    234 rdf:type schema:CreativeWork
    235 https://doi.org/10.1016/s0550-3213(98)00426-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1042398666
    236 rdf:type schema:CreativeWork
    237 https://doi.org/10.1016/s0550-3213(99)00796-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030524649
    238 rdf:type schema:CreativeWork
    239 https://doi.org/10.1063/1.1374448 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057700303
    240 rdf:type schema:CreativeWork
    241 https://doi.org/10.1063/1.4826603 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019911938
    242 rdf:type schema:CreativeWork
    243 https://doi.org/10.1088/0264-9381/20/23/009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021753822
    244 rdf:type schema:CreativeWork
    245 https://doi.org/10.1088/1751-8113/42/33/335402 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016995997
    246 rdf:type schema:CreativeWork
    247 https://doi.org/10.1090/pspum/090/01523 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089187677
    248 rdf:type schema:CreativeWork
    249 https://doi.org/10.1090/s0065-9266-2011-00630-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059337554
    250 rdf:type schema:CreativeWork
    251 https://doi.org/10.1103/physrevd.52.r5412 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001776675
    252 rdf:type schema:CreativeWork
    253 https://doi.org/10.1103/physrevd.90.041902 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026553148
    254 rdf:type schema:CreativeWork
    255 https://doi.org/10.1103/physrevlett.114.121601 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023919274
    256 rdf:type schema:CreativeWork
    257 https://doi.org/10.1103/physrevlett.98.211602 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042261907
    258 rdf:type schema:CreativeWork
    259 https://doi.org/10.1142/s0129167x95000146 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062903453
    260 rdf:type schema:CreativeWork
    261 https://doi.org/10.1142/s0217751x89000972 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062928738
    262 rdf:type schema:CreativeWork
    263 https://doi.org/10.1215/00127094-3129595 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064411471
    264 rdf:type schema:CreativeWork
    265 https://doi.org/10.1353/ajm.2013.0031 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019918015
    266 rdf:type schema:CreativeWork
    267 https://doi.org/10.4310/atmp.2011.v15.n1.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072457321
    268 rdf:type schema:CreativeWork
    269 https://doi.org/10.4310/cntp.2010.v4.n1.a3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072459478
    270 rdf:type schema:CreativeWork
    271 https://doi.org/10.4310/cntp.2012.v6.n2.a4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072459517
    272 rdf:type schema:CreativeWork
    273 https://doi.org/10.4310/cntp.2012.v6.n4.a5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072459526
    274 rdf:type schema:CreativeWork
    275 https://doi.org/10.4310/jdg/1497405629 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086017437
    276 rdf:type schema:CreativeWork
    277 https://www.grid.ac/institutes/grid.457338.e schema:alternateName L'Institut de physique théorique
    278 schema:name IPhT, CEA, Saclay, 91191, Gif-sur-Yvette, France
    279 rdf:type schema:Organization
    280 https://www.grid.ac/institutes/grid.462669.9 schema:alternateName Laboratoire Charles Coulomb
    281 schema:name Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34095, Montpellier, France
    282 rdf:type schema:Organization
    283 https://www.grid.ac/institutes/grid.463942.e schema:alternateName Laboratory of Theoretical and High Energy Physics
    284 schema:name CERN PH-TH, Case C01600, CERN, 1211, Geneva 23, Switzerland
    285 Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France
    286 rdf:type schema:Organization
    287 https://www.grid.ac/institutes/grid.8217.c schema:alternateName Trinity College Dublin
    288 schema:name School of Mathematics, Trinity College, Dublin 2, Ireland
    289 rdf:type schema:Organization
     




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


    ...