Box graphs and singular fibers View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-05-12

AUTHORS

Hirotaka Hayashi, Craig Lawrie, David R. Morrison, Sakura Schafer-Nameki

ABSTRACT

We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping” of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E6, E7 and E8. More... »

PAGES

48

References to SciGraph publications

  • 2013-07-18. Effective action of 6D F-theory with U(1) factors: rational sections make Chern-Simons terms jump in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-07-05. On singular fibres in F-theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-01-05. Matter and singularities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-07-12. F-theory GUT vacua on compact Calabi-Yau fourfolds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-03-18. U(1) symmetries in F-theory GUTs with multiple sections in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-04-02. Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factors in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-02-18. Anomaly cancellation and abelian gauge symmetries in F-theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-11-21. Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-04-10. The Tate form on steroids: resolution and higher codimension fibers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-10-08. Phases, flops and F-theory: SU(5) gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-09-27. New global F-theory GUTs with U(1) symmetries in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-12-16. Geometric engineering in toric F-theory and GUTs with U(1) gauge factors in JOURNAL OF HIGH ENERGY PHYSICS
  • 1964-12. Modèles minimaux des variétés abéliennes sur les corps locaux et globaux in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2002-06-06. Codimension-three bundle singularities in F-theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-06-17. F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-10-18. F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-07-22. Non-simply-connected gauge groups and rational points on elliptic curves in JOURNAL OF HIGH ENERGY PHYSICS
  • 1985-09. The birational geometry of surfaces with rational double points in MATHEMATISCHE ANNALEN
  • 1980. Surfaces de Del Pezzo — I in SÉMINAIRE SUR LES SINGULARITÉS DES SURFACES
  • 2014-03-04. Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1)×U(1)×U(1) gauge symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-03-09. F-theory fluxes, chirality and Chern-Simons theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1991-03. On minimal models of elliptic threefolds in MATHEMATISCHE ANNALEN
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep05(2014)048

    DOI

    http://dx.doi.org/10.1007/jhep05(2014)048

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1025452396


    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": "Instituto de Fisica Teorica UAM/CSIS, Calle Nicolas Cabrera, Cantoblanco, 28049, Madrid, Spain", 
              "id": "http://www.grid.ac/institutes/grid.501798.2", 
              "name": [
                "Instituto de Fisica Teorica UAM/CSIS, Calle Nicolas Cabrera, Cantoblanco, 28049, Madrid, Spain"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hayashi", 
            "givenName": "Hirotaka", 
            "id": "sg:person.012413203443.40", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012413203443.40"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, King\u2019s College London, The Strand, WC2R 2LS, London, United Kingdom", 
              "id": "http://www.grid.ac/institutes/grid.13097.3c", 
              "name": [
                "Department of Mathematics, King\u2019s College London, The Strand, WC2R 2LS, London, United Kingdom"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Lawrie", 
            "givenName": "Craig", 
            "id": "sg:person.011125030216.92", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011125030216.92"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Departments of Mathematics and Physics, University of California, 93106, Santa Barbara, CA, United States", 
              "id": "http://www.grid.ac/institutes/grid.133342.4", 
              "name": [
                "Departments of Mathematics and Physics, University of California, 93106, Santa Barbara, CA, United States"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Morrison", 
            "givenName": "David R.", 
            "id": "sg:person.011316747253.35", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011316747253.35"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, King\u2019s College London, The Strand, WC2R 2LS, London, United Kingdom", 
              "id": "http://www.grid.ac/institutes/grid.13097.3c", 
              "name": [
                "Department of Mathematics, King\u2019s College London, The Strand, WC2R 2LS, London, United Kingdom"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Schafer-Nameki", 
            "givenName": "Sakura", 
            "id": "sg:person.015352352421.76", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015352352421.76"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/jhep01(2012)022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045044378", 
              "https://doi.org/10.1007/jhep01(2012)022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2011)098", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039895775", 
              "https://doi.org/10.1007/jhep11(2011)098"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2014)010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000212825", 
              "https://doi.org/10.1007/jhep04(2014)010"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2002/06/014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038171854", 
              "https://doi.org/10.1088/1126-6708/2002/06/014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01456077", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050191285", 
              "https://doi.org/10.1007/bf01456077"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep10(2012)128", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010261260", 
              "https://doi.org/10.1007/jhep10(2012)128"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/1998/07/012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002419177", 
              "https://doi.org/10.1088/1126-6708/1998/07/012"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2013)101", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011286316", 
              "https://doi.org/10.1007/jhep02(2013)101"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2013)067", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014002142", 
              "https://doi.org/10.1007/jhep06(2013)067"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2012)027", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003639562", 
              "https://doi.org/10.1007/jhep03(2012)027"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2013)154", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030143543", 
              "https://doi.org/10.1007/jhep09(2013)154"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2013)115", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043675760", 
              "https://doi.org/10.1007/jhep07(2013)115"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0085875", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010369518", 
              "https://doi.org/10.1007/bfb0085875"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2010)037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030229004", 
              "https://doi.org/10.1007/jhep07(2010)037"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2014)021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050297831", 
              "https://doi.org/10.1007/jhep03(2014)021"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02684271", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017043060", 
              "https://doi.org/10.1007/bf02684271"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2013)031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002060948", 
              "https://doi.org/10.1007/jhep07(2013)031"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2013)098", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023013759", 
              "https://doi.org/10.1007/jhep03(2013)098"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01459246", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008923720", 
              "https://doi.org/10.1007/bf01459246"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep12(2013)069", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015348597", 
              "https://doi.org/10.1007/jhep12(2013)069"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep10(2013)046", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050856190", 
              "https://doi.org/10.1007/jhep10(2013)046"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2013)061", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027233011", 
              "https://doi.org/10.1007/jhep04(2013)061"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2014-05-12", 
        "datePublishedReg": "2014-05-12", 
        "description": "We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$ \\mathcal{N} $\\end{document} = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as \u201cflopping\u201d of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E6, E7 and E8.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/jhep05(2014)048", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.3495214", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.2751607", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "5", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2014"
          }
        ], 
        "keywords": [
          "Calabi-Yau fourfolds", 
          "Weierstrass model", 
          "elliptic Calabi-Yau fourfolds", 
          "reductive Lie group", 
          "supersymmetric gauge theories", 
          "low energy effective theory", 
          "Lie algebra", 
          "Lie groups", 
          "crepant resolutions", 
          "geometric point", 
          "singular model", 
          "singular fibers", 
          "Coulomb branch", 
          "matter representations", 
          "flop transition", 
          "gauge theory", 
          "codimension two", 
          "matter multiplets", 
          "box graphs", 
          "effective curves", 
          "effective theory", 
          "entire network", 
          "theory", 
          "graph", 
          "representation graph", 
          "convex paths", 
          "algebra", 
          "concise description", 
          "Kodaira", 
          "simple interpretation", 
          "network", 
          "representation", 
          "model", 
          "E8", 
          "description", 
          "class", 
          "geometry", 
          "particular resolution", 
          "generator", 
          "multiplets", 
          "path", 
          "terms", 
          "cone", 
          "point", 
          "fourfold", 
          "two", 
          "branches", 
          "curves", 
          "types", 
          "interpretation", 
          "analysis", 
          "structure", 
          "transition", 
          "resolution", 
          "view", 
          "sections", 
          "E6", 
          "phase", 
          "E7", 
          "matter", 
          "group", 
          "fibers", 
          "fiber types", 
          "higher codimension fibers", 
          "codimension fibers", 
          "energy effective theory", 
          "actual flop transitions", 
          "network of phases", 
          "specific Lie algebra", 
          "singular elliptic Calabi-Yau fourfolds"
        ], 
        "name": "Box graphs and singular fibers", 
        "pagination": "48", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1025452396"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep05(2014)048"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep05(2014)048", 
          "https://app.dimensions.ai/details/publication/pub.1025452396"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:33", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_624.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/jhep05(2014)048"
      }
    ]
     

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

    HOW TO GET THIS DATA PROGRAMMATICALLY:

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

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2014)048'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2014)048'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2014)048'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep05(2014)048'


     

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

    247 TRIPLES      22 PREDICATES      117 URIs      87 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep05(2014)048 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N66e0e12b2b50437193ba93764ea91ba6
    4 schema:citation sg:pub.10.1007/bf01456077
    5 sg:pub.10.1007/bf01459246
    6 sg:pub.10.1007/bf02684271
    7 sg:pub.10.1007/bfb0085875
    8 sg:pub.10.1007/jhep01(2012)022
    9 sg:pub.10.1007/jhep02(2013)101
    10 sg:pub.10.1007/jhep03(2012)027
    11 sg:pub.10.1007/jhep03(2013)098
    12 sg:pub.10.1007/jhep03(2014)021
    13 sg:pub.10.1007/jhep04(2013)061
    14 sg:pub.10.1007/jhep04(2014)010
    15 sg:pub.10.1007/jhep06(2013)067
    16 sg:pub.10.1007/jhep07(2010)037
    17 sg:pub.10.1007/jhep07(2013)031
    18 sg:pub.10.1007/jhep07(2013)115
    19 sg:pub.10.1007/jhep09(2013)154
    20 sg:pub.10.1007/jhep10(2012)128
    21 sg:pub.10.1007/jhep10(2013)046
    22 sg:pub.10.1007/jhep11(2011)098
    23 sg:pub.10.1007/jhep12(2013)069
    24 sg:pub.10.1088/1126-6708/1998/07/012
    25 sg:pub.10.1088/1126-6708/2002/06/014
    26 schema:datePublished 2014-05-12
    27 schema:datePublishedReg 2014-05-12
    28 schema:description We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping” of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E6, E7 and E8.
    29 schema:genre article
    30 schema:inLanguage en
    31 schema:isAccessibleForFree true
    32 schema:isPartOf N39496b397b144b739456b5cfad1b1421
    33 N569e7362ac1c400c80ba164aca4327aa
    34 sg:journal.1052482
    35 schema:keywords Calabi-Yau fourfolds
    36 Coulomb branch
    37 E6
    38 E7
    39 E8
    40 Kodaira
    41 Lie algebra
    42 Lie groups
    43 Weierstrass model
    44 actual flop transitions
    45 algebra
    46 analysis
    47 box graphs
    48 branches
    49 class
    50 codimension fibers
    51 codimension two
    52 concise description
    53 cone
    54 convex paths
    55 crepant resolutions
    56 curves
    57 description
    58 effective curves
    59 effective theory
    60 elliptic Calabi-Yau fourfolds
    61 energy effective theory
    62 entire network
    63 fiber types
    64 fibers
    65 flop transition
    66 fourfold
    67 gauge theory
    68 generator
    69 geometric point
    70 geometry
    71 graph
    72 group
    73 higher codimension fibers
    74 interpretation
    75 low energy effective theory
    76 matter
    77 matter multiplets
    78 matter representations
    79 model
    80 multiplets
    81 network
    82 network of phases
    83 particular resolution
    84 path
    85 phase
    86 point
    87 reductive Lie group
    88 representation
    89 representation graph
    90 resolution
    91 sections
    92 simple interpretation
    93 singular elliptic Calabi-Yau fourfolds
    94 singular fibers
    95 singular model
    96 specific Lie algebra
    97 structure
    98 supersymmetric gauge theories
    99 terms
    100 theory
    101 transition
    102 two
    103 types
    104 view
    105 schema:name Box graphs and singular fibers
    106 schema:pagination 48
    107 schema:productId N99b2abab79954f8c87766fe50f3d700a
    108 Nc8581a3e55e743878545d7d8b298ca30
    109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025452396
    110 https://doi.org/10.1007/jhep05(2014)048
    111 schema:sdDatePublished 2022-01-01T18:33
    112 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    113 schema:sdPublisher N71baf6c6d5164cde87f304173b0f1872
    114 schema:url https://doi.org/10.1007/jhep05(2014)048
    115 sgo:license sg:explorer/license/
    116 sgo:sdDataset articles
    117 rdf:type schema:ScholarlyArticle
    118 N1670cfb52e3c45f4a2e6d15b1b97ea3a rdf:first sg:person.011125030216.92
    119 rdf:rest Ndd3029382a4e4bf5b03b693e28199fbc
    120 N1cc420641dd3459682142e11235a2789 rdf:first sg:person.015352352421.76
    121 rdf:rest rdf:nil
    122 N39496b397b144b739456b5cfad1b1421 schema:issueNumber 5
    123 rdf:type schema:PublicationIssue
    124 N569e7362ac1c400c80ba164aca4327aa schema:volumeNumber 2014
    125 rdf:type schema:PublicationVolume
    126 N66e0e12b2b50437193ba93764ea91ba6 rdf:first sg:person.012413203443.40
    127 rdf:rest N1670cfb52e3c45f4a2e6d15b1b97ea3a
    128 N71baf6c6d5164cde87f304173b0f1872 schema:name Springer Nature - SN SciGraph project
    129 rdf:type schema:Organization
    130 N99b2abab79954f8c87766fe50f3d700a schema:name dimensions_id
    131 schema:value pub.1025452396
    132 rdf:type schema:PropertyValue
    133 Nc8581a3e55e743878545d7d8b298ca30 schema:name doi
    134 schema:value 10.1007/jhep05(2014)048
    135 rdf:type schema:PropertyValue
    136 Ndd3029382a4e4bf5b03b693e28199fbc rdf:first sg:person.011316747253.35
    137 rdf:rest N1cc420641dd3459682142e11235a2789
    138 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    139 schema:name Mathematical Sciences
    140 rdf:type schema:DefinedTerm
    141 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    142 schema:name Pure Mathematics
    143 rdf:type schema:DefinedTerm
    144 sg:grant.2751607 http://pending.schema.org/fundedItem sg:pub.10.1007/jhep05(2014)048
    145 rdf:type schema:MonetaryGrant
    146 sg:grant.3495214 http://pending.schema.org/fundedItem sg:pub.10.1007/jhep05(2014)048
    147 rdf:type schema:MonetaryGrant
    148 sg:journal.1052482 schema:issn 1029-8479
    149 1126-6708
    150 schema:name Journal of High Energy Physics
    151 schema:publisher Springer Nature
    152 rdf:type schema:Periodical
    153 sg:person.011125030216.92 schema:affiliation grid-institutes:grid.13097.3c
    154 schema:familyName Lawrie
    155 schema:givenName Craig
    156 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011125030216.92
    157 rdf:type schema:Person
    158 sg:person.011316747253.35 schema:affiliation grid-institutes:grid.133342.4
    159 schema:familyName Morrison
    160 schema:givenName David R.
    161 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011316747253.35
    162 rdf:type schema:Person
    163 sg:person.012413203443.40 schema:affiliation grid-institutes:grid.501798.2
    164 schema:familyName Hayashi
    165 schema:givenName Hirotaka
    166 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012413203443.40
    167 rdf:type schema:Person
    168 sg:person.015352352421.76 schema:affiliation grid-institutes:grid.13097.3c
    169 schema:familyName Schafer-Nameki
    170 schema:givenName Sakura
    171 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015352352421.76
    172 rdf:type schema:Person
    173 sg:pub.10.1007/bf01456077 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050191285
    174 https://doi.org/10.1007/bf01456077
    175 rdf:type schema:CreativeWork
    176 sg:pub.10.1007/bf01459246 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008923720
    177 https://doi.org/10.1007/bf01459246
    178 rdf:type schema:CreativeWork
    179 sg:pub.10.1007/bf02684271 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017043060
    180 https://doi.org/10.1007/bf02684271
    181 rdf:type schema:CreativeWork
    182 sg:pub.10.1007/bfb0085875 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010369518
    183 https://doi.org/10.1007/bfb0085875
    184 rdf:type schema:CreativeWork
    185 sg:pub.10.1007/jhep01(2012)022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045044378
    186 https://doi.org/10.1007/jhep01(2012)022
    187 rdf:type schema:CreativeWork
    188 sg:pub.10.1007/jhep02(2013)101 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011286316
    189 https://doi.org/10.1007/jhep02(2013)101
    190 rdf:type schema:CreativeWork
    191 sg:pub.10.1007/jhep03(2012)027 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003639562
    192 https://doi.org/10.1007/jhep03(2012)027
    193 rdf:type schema:CreativeWork
    194 sg:pub.10.1007/jhep03(2013)098 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023013759
    195 https://doi.org/10.1007/jhep03(2013)098
    196 rdf:type schema:CreativeWork
    197 sg:pub.10.1007/jhep03(2014)021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050297831
    198 https://doi.org/10.1007/jhep03(2014)021
    199 rdf:type schema:CreativeWork
    200 sg:pub.10.1007/jhep04(2013)061 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027233011
    201 https://doi.org/10.1007/jhep04(2013)061
    202 rdf:type schema:CreativeWork
    203 sg:pub.10.1007/jhep04(2014)010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000212825
    204 https://doi.org/10.1007/jhep04(2014)010
    205 rdf:type schema:CreativeWork
    206 sg:pub.10.1007/jhep06(2013)067 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014002142
    207 https://doi.org/10.1007/jhep06(2013)067
    208 rdf:type schema:CreativeWork
    209 sg:pub.10.1007/jhep07(2010)037 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030229004
    210 https://doi.org/10.1007/jhep07(2010)037
    211 rdf:type schema:CreativeWork
    212 sg:pub.10.1007/jhep07(2013)031 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002060948
    213 https://doi.org/10.1007/jhep07(2013)031
    214 rdf:type schema:CreativeWork
    215 sg:pub.10.1007/jhep07(2013)115 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043675760
    216 https://doi.org/10.1007/jhep07(2013)115
    217 rdf:type schema:CreativeWork
    218 sg:pub.10.1007/jhep09(2013)154 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030143543
    219 https://doi.org/10.1007/jhep09(2013)154
    220 rdf:type schema:CreativeWork
    221 sg:pub.10.1007/jhep10(2012)128 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010261260
    222 https://doi.org/10.1007/jhep10(2012)128
    223 rdf:type schema:CreativeWork
    224 sg:pub.10.1007/jhep10(2013)046 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050856190
    225 https://doi.org/10.1007/jhep10(2013)046
    226 rdf:type schema:CreativeWork
    227 sg:pub.10.1007/jhep11(2011)098 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039895775
    228 https://doi.org/10.1007/jhep11(2011)098
    229 rdf:type schema:CreativeWork
    230 sg:pub.10.1007/jhep12(2013)069 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015348597
    231 https://doi.org/10.1007/jhep12(2013)069
    232 rdf:type schema:CreativeWork
    233 sg:pub.10.1088/1126-6708/1998/07/012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002419177
    234 https://doi.org/10.1088/1126-6708/1998/07/012
    235 rdf:type schema:CreativeWork
    236 sg:pub.10.1088/1126-6708/2002/06/014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038171854
    237 https://doi.org/10.1088/1126-6708/2002/06/014
    238 rdf:type schema:CreativeWork
    239 grid-institutes:grid.13097.3c schema:alternateName Department of Mathematics, King’s College London, The Strand, WC2R 2LS, London, United Kingdom
    240 schema:name Department of Mathematics, King’s College London, The Strand, WC2R 2LS, London, United Kingdom
    241 rdf:type schema:Organization
    242 grid-institutes:grid.133342.4 schema:alternateName Departments of Mathematics and Physics, University of California, 93106, Santa Barbara, CA, United States
    243 schema:name Departments of Mathematics and Physics, University of California, 93106, Santa Barbara, CA, United States
    244 rdf:type schema:Organization
    245 grid-institutes:grid.501798.2 schema:alternateName Instituto de Fisica Teorica UAM/CSIS, Calle Nicolas Cabrera, Cantoblanco, 28049, Madrid, Spain
    246 schema:name Instituto de Fisica Teorica UAM/CSIS, Calle Nicolas Cabrera, Cantoblanco, 28049, Madrid, Spain
    247 rdf:type schema:Organization
     




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


    ...