The Topological Vertex View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2004-09-24

AUTHORS

Mina Aganagic, Albrecht Klemm, Marcos Mariño, Cumrun Vafa

ABSTRACT

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization. More... »

PAGES

425-478

References to SciGraph publications

  • 1995. Enumeration of Rational Curves Via Torus Actions in THE MODULI SPACE OF CURVES
  • 1989-09. Quantum field theory and the Jones polynomial in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2000-11-03. Knots, links and branes at large N in JOURNAL OF HIGH ENERGY PHYSICS
  • 1988-09. Topological sigma models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-07. Calibrated geometries in ACTA MATHEMATICA
  • 1998-01-06. Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-02-06. Matrix model as a mirror of Chern-Simons theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-04-09. All Loop Topological String Amplitudes from Chern-Simons Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1995. Chern-Simons gauge theory as a string theory in THE FLOER MEMORIAL VOLUME
  • 1994-10. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-03. Polynomial Invariants for Torus Knots¶and Topological Strings in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-004-1162-z

    DOI

    http://dx.doi.org/10.1007/s00220-004-1162-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1047832310


    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": "Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA", 
              "id": "http://www.grid.ac/institutes/grid.38142.3c", 
              "name": [
                "Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Aganagic", 
            "givenName": "Mina", 
            "id": "sg:person.0677553504.21", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0677553504.21"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, 10115, Berlin, Germany", 
              "id": "http://www.grid.ac/institutes/grid.7468.d", 
              "name": [
                "Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, 10115, Berlin, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Klemm", 
            "givenName": "Albrecht", 
            "id": "sg:person.07535601751.07", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07535601751.07"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Theory Division, CERN, Geneva 23, 1211, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.9132.9", 
              "name": [
                "Theory Division, CERN, Geneva 23, 1211, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Mari\u00f1o", 
            "givenName": "Marcos", 
            "id": "sg:person.014141535632.26", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014141535632.26"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "California Institute of Technology, 452-48, 91125, Pasadena, CA, USA", 
              "id": "http://www.grid.ac/institutes/grid.20861.3d", 
              "name": [
                "Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA", 
                "California Institute of Technology, 452-48, 91125, Pasadena, CA, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Vafa", 
            "givenName": "Cumrun", 
            "id": "sg:person.014523005000.99", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014523005000.99"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-1-4612-4264-2_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006492963", 
              "https://doi.org/10.1007/978-1-4612-4264-2_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200100374", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028849541", 
              "https://doi.org/10.1007/s002200100374"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-0348-9217-9_28", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006797177", 
              "https://doi.org/10.1007/978-3-0348-9217-9_28"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099774", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049578045", 
              "https://doi.org/10.1007/bf02099774"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02392726", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036490061", 
              "https://doi.org/10.1007/bf02392726"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2000/11/007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000253180", 
              "https://doi.org/10.1088/1126-6708/2000/11/007"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-004-1067-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040658724", 
              "https://doi.org/10.1007/s00220-004-1067-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/1998/01/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026223761", 
              "https://doi.org/10.1088/1126-6708/1998/01/002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01217730", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033035951", 
              "https://doi.org/10.1007/bf01217730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2004/02/010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009823693", 
              "https://doi.org/10.1088/1126-6708/2004/02/010"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01466725", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033100303", 
              "https://doi.org/10.1007/bf01466725"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2004-09-24", 
        "datePublishedReg": "2004-09-24", 
        "description": "We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of K\u00e4hler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00220-004-1162-z", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "254"
          }
        ], 
        "keywords": [
          "Riemann surface", 
          "toric Calabi-Yau threefolds", 
          "cubic field theory", 
          "Calabi-Yau threefolds", 
          "genus amplitudes", 
          "field theory", 
          "Calabi-Yau", 
          "K\u00e4hler class", 
          "topological vertex", 
          "Schwinger parameters", 
          "Feynman diagrams", 
          "chiral bosons", 
          "only degree", 
          "chiral scalar", 
          "theory", 
          "topology", 
          "threefold", 
          "bosonization", 
          "branes", 
          "scalar", 
          "computation", 
          "fermions", 
          "vertices", 
          "amplitude", 
          "model mirrors", 
          "bosons", 
          "class", 
          "diagram", 
          "freedom", 
          "parameters", 
          "model", 
          "mirror", 
          "setup", 
          "surface", 
          "results", 
          "degree", 
          "role"
        ], 
        "name": "The Topological Vertex", 
        "pagination": "425-478", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1047832310"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00220-004-1162-z"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00220-004-1162-z", 
          "https://app.dimensions.ai/details/publication/pub.1047832310"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-05-10T09:52", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_387.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00220-004-1162-z"
      }
    ]
     

    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/s00220-004-1162-z'

    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/s00220-004-1162-z'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1162-z'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1162-z'


     

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

    170 TRIPLES      22 PREDICATES      73 URIs      54 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00220-004-1162-z schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N1ed145cec3a94e5cb85a4abdb2addced
    4 schema:citation sg:pub.10.1007/978-1-4612-4264-2_12
    5 sg:pub.10.1007/978-3-0348-9217-9_28
    6 sg:pub.10.1007/bf01217730
    7 sg:pub.10.1007/bf01466725
    8 sg:pub.10.1007/bf02099774
    9 sg:pub.10.1007/bf02392726
    10 sg:pub.10.1007/s00220-004-1067-x
    11 sg:pub.10.1007/s002200100374
    12 sg:pub.10.1088/1126-6708/1998/01/002
    13 sg:pub.10.1088/1126-6708/2000/11/007
    14 sg:pub.10.1088/1126-6708/2004/02/010
    15 schema:datePublished 2004-09-24
    16 schema:datePublishedReg 2004-09-24
    17 schema:description We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.
    18 schema:genre article
    19 schema:inLanguage en
    20 schema:isAccessibleForFree true
    21 schema:isPartOf N81bee699ee6444adb5278630d0c9137b
    22 Ne2b12a1d233f461595840d17151878a3
    23 sg:journal.1136216
    24 schema:keywords Calabi-Yau
    25 Calabi-Yau threefolds
    26 Feynman diagrams
    27 Kähler class
    28 Riemann surface
    29 Schwinger parameters
    30 amplitude
    31 bosonization
    32 bosons
    33 branes
    34 chiral bosons
    35 chiral scalar
    36 class
    37 computation
    38 cubic field theory
    39 degree
    40 diagram
    41 fermions
    42 field theory
    43 freedom
    44 genus amplitudes
    45 mirror
    46 model
    47 model mirrors
    48 only degree
    49 parameters
    50 results
    51 role
    52 scalar
    53 setup
    54 surface
    55 theory
    56 threefold
    57 topological vertex
    58 topology
    59 toric Calabi-Yau threefolds
    60 vertices
    61 schema:name The Topological Vertex
    62 schema:pagination 425-478
    63 schema:productId N34706f31bad64133a65d19c21e721dbf
    64 Ne6b1829375e5429694da613963b803ff
    65 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047832310
    66 https://doi.org/10.1007/s00220-004-1162-z
    67 schema:sdDatePublished 2022-05-10T09:52
    68 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    69 schema:sdPublisher N845f57eb552d42d0a8c3f66d5edc7b90
    70 schema:url https://doi.org/10.1007/s00220-004-1162-z
    71 sgo:license sg:explorer/license/
    72 sgo:sdDataset articles
    73 rdf:type schema:ScholarlyArticle
    74 N1ed145cec3a94e5cb85a4abdb2addced rdf:first sg:person.0677553504.21
    75 rdf:rest N3ac2183eb9aa42f8af0680e7f9958e83
    76 N2a95408bb8cd4b85aaabeea27fdcdd1e rdf:first sg:person.014141535632.26
    77 rdf:rest N9d4171ff81984cf88a5cca01f01915d5
    78 N34706f31bad64133a65d19c21e721dbf schema:name doi
    79 schema:value 10.1007/s00220-004-1162-z
    80 rdf:type schema:PropertyValue
    81 N3ac2183eb9aa42f8af0680e7f9958e83 rdf:first sg:person.07535601751.07
    82 rdf:rest N2a95408bb8cd4b85aaabeea27fdcdd1e
    83 N81bee699ee6444adb5278630d0c9137b schema:issueNumber 2
    84 rdf:type schema:PublicationIssue
    85 N845f57eb552d42d0a8c3f66d5edc7b90 schema:name Springer Nature - SN SciGraph project
    86 rdf:type schema:Organization
    87 N9d4171ff81984cf88a5cca01f01915d5 rdf:first sg:person.014523005000.99
    88 rdf:rest rdf:nil
    89 Ne2b12a1d233f461595840d17151878a3 schema:volumeNumber 254
    90 rdf:type schema:PublicationVolume
    91 Ne6b1829375e5429694da613963b803ff schema:name dimensions_id
    92 schema:value pub.1047832310
    93 rdf:type schema:PropertyValue
    94 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    95 schema:name Mathematical Sciences
    96 rdf:type schema:DefinedTerm
    97 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    98 schema:name Pure Mathematics
    99 rdf:type schema:DefinedTerm
    100 sg:journal.1136216 schema:issn 0010-3616
    101 1432-0916
    102 schema:name Communications in Mathematical Physics
    103 schema:publisher Springer Nature
    104 rdf:type schema:Periodical
    105 sg:person.014141535632.26 schema:affiliation grid-institutes:grid.9132.9
    106 schema:familyName Mariño
    107 schema:givenName Marcos
    108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014141535632.26
    109 rdf:type schema:Person
    110 sg:person.014523005000.99 schema:affiliation grid-institutes:grid.20861.3d
    111 schema:familyName Vafa
    112 schema:givenName Cumrun
    113 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014523005000.99
    114 rdf:type schema:Person
    115 sg:person.0677553504.21 schema:affiliation grid-institutes:grid.38142.3c
    116 schema:familyName Aganagic
    117 schema:givenName Mina
    118 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0677553504.21
    119 rdf:type schema:Person
    120 sg:person.07535601751.07 schema:affiliation grid-institutes:grid.7468.d
    121 schema:familyName Klemm
    122 schema:givenName Albrecht
    123 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07535601751.07
    124 rdf:type schema:Person
    125 sg:pub.10.1007/978-1-4612-4264-2_12 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006492963
    126 https://doi.org/10.1007/978-1-4612-4264-2_12
    127 rdf:type schema:CreativeWork
    128 sg:pub.10.1007/978-3-0348-9217-9_28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006797177
    129 https://doi.org/10.1007/978-3-0348-9217-9_28
    130 rdf:type schema:CreativeWork
    131 sg:pub.10.1007/bf01217730 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033035951
    132 https://doi.org/10.1007/bf01217730
    133 rdf:type schema:CreativeWork
    134 sg:pub.10.1007/bf01466725 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033100303
    135 https://doi.org/10.1007/bf01466725
    136 rdf:type schema:CreativeWork
    137 sg:pub.10.1007/bf02099774 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049578045
    138 https://doi.org/10.1007/bf02099774
    139 rdf:type schema:CreativeWork
    140 sg:pub.10.1007/bf02392726 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036490061
    141 https://doi.org/10.1007/bf02392726
    142 rdf:type schema:CreativeWork
    143 sg:pub.10.1007/s00220-004-1067-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1040658724
    144 https://doi.org/10.1007/s00220-004-1067-x
    145 rdf:type schema:CreativeWork
    146 sg:pub.10.1007/s002200100374 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028849541
    147 https://doi.org/10.1007/s002200100374
    148 rdf:type schema:CreativeWork
    149 sg:pub.10.1088/1126-6708/1998/01/002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026223761
    150 https://doi.org/10.1088/1126-6708/1998/01/002
    151 rdf:type schema:CreativeWork
    152 sg:pub.10.1088/1126-6708/2000/11/007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000253180
    153 https://doi.org/10.1088/1126-6708/2000/11/007
    154 rdf:type schema:CreativeWork
    155 sg:pub.10.1088/1126-6708/2004/02/010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009823693
    156 https://doi.org/10.1088/1126-6708/2004/02/010
    157 rdf:type schema:CreativeWork
    158 grid-institutes:grid.20861.3d schema:alternateName California Institute of Technology, 452-48, 91125, Pasadena, CA, USA
    159 schema:name California Institute of Technology, 452-48, 91125, Pasadena, CA, USA
    160 Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA
    161 rdf:type schema:Organization
    162 grid-institutes:grid.38142.3c schema:alternateName Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA
    163 schema:name Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, USA
    164 rdf:type schema:Organization
    165 grid-institutes:grid.7468.d schema:alternateName Institut für Physik, Humboldt-Universität zu Berlin, 10115, Berlin, Germany
    166 schema:name Institut für Physik, Humboldt-Universität zu Berlin, 10115, Berlin, Germany
    167 rdf:type schema:Organization
    168 grid-institutes:grid.9132.9 schema:alternateName Theory Division, CERN, Geneva 23, 1211, Switzerland
    169 schema:name Theory Division, CERN, Geneva 23, 1211, Switzerland
    170 rdf:type schema:Organization
     




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


    ...