Symmetries of Toric Duality View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2002-12-27

AUTHORS

Bo Feng, Sebastián Franco, Amihay Hanany, Yang-Hui He

ABSTRACT

This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone. More... »

PAGES

076

References to SciGraph publications

  • 2002-04-04. Quiver Theories from D6-branes via Mirror Symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-12-30. Toric duality as Seiberg duality and brane diamonds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-12-03. Toric duality is Seiberg duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-01-15. Phases of supersymmetric D-branes on Kähler manifolds and the McKay correspondence in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-08-17. Phase structure of D-brane gauge theories and toric duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-04-29. Reverse geometric engineering of singularities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-02-06. D-branes on Calabi-Yau manifolds and helices in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-09-05. Stability of quiver representations and topology change in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1088/1126-6708/2002/12/076

    DOI

    http://dx.doi.org/10.1088/1126-6708/2002/12/076

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1031433556


    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": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Feng", 
            "givenName": "Bo", 
            "id": "sg:person.0614443717.35", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0614443717.35"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Franco", 
            "givenName": "Sebasti\u00e1n", 
            "id": "sg:person.013105053075.99", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013105053075.99"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hanany", 
            "givenName": "Amihay", 
            "id": "sg:person.012155553275.80", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012155553275.80"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Massachusetts Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.116068.8", 
              "name": [
                "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "He", 
            "givenName": "Yang-Hui", 
            "id": "sg:person.010540777615.39", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010540777615.39"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/s0550-3213(99)00700-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000268900"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(02)00078-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001677489"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2002/04/052", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003711632", 
              "https://doi.org/10.1088/1126-6708/2002/04/052"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(93)90033-l", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004765127"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(93)90033-l", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004765127"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/12/035", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007275558", 
              "https://doi.org/10.1088/1126-6708/2001/12/035"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/08/040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008510756", 
              "https://doi.org/10.1088/1126-6708/2001/08/040"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(97)00517-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016900381"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(00)00699-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018210546"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(02)00762-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019013456"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/01/018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021289806", 
              "https://doi.org/10.1088/1126-6708/2001/01/018"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2002/04/009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023292462", 
              "https://doi.org/10.1088/1126-6708/2002/04/009"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(01)00296-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027856859"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(99)00646-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033701969"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(01)00062-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036756880"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/12/001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040554299", 
              "https://doi.org/10.1088/1126-6708/2001/12/001"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(98)00246-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050310900"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/09/008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050733879", 
              "https://doi.org/10.1088/1126-6708/2001/09/008"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/02/008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053682608", 
              "https://doi.org/10.1088/1126-6708/2001/02/008"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.1999.v3.n1.a1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072456932"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.2000.v4.n4.a1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072457001"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.2000.v4.n4.a2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072457002"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2002-12-27", 
        "datePublishedReg": "2002-12-27", 
        "description": "This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1088/1126-6708/2002/12/076", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "12", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2002"
          }
        ], 
        "name": "Symmetries of Toric Duality", 
        "pagination": "076", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "95be04cba0edc527f0986ca8fd7e90ff337f4b81624b0742203466ad64cfd6e7"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1088/1126-6708/2002/12/076"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1031433556"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1088/1126-6708/2002/12/076", 
          "https://app.dimensions.ai/details/publication/pub.1031433556"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T21:12", 
        "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/v90/0000000001_0000000264/records_8687_00000262.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://iopscience.iop.org/article/10.1088/1126-6708/2002/12/076/meta"
      }
    ]
     

    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.10.1088/1126-6708/2002/12/076'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2002/12/076'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2002/12/076'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2002/12/076'


     

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

    153 TRIPLES      21 PREDICATES      47 URIs      18 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1088/1126-6708/2002/12/076 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N8d00dd77bab640408bc3a5e182d17846
    4 schema:citation sg:pub.10.1088/1126-6708/2001/01/018
    5 sg:pub.10.1088/1126-6708/2001/02/008
    6 sg:pub.10.1088/1126-6708/2001/08/040
    7 sg:pub.10.1088/1126-6708/2001/09/008
    8 sg:pub.10.1088/1126-6708/2001/12/001
    9 sg:pub.10.1088/1126-6708/2001/12/035
    10 sg:pub.10.1088/1126-6708/2002/04/009
    11 sg:pub.10.1088/1126-6708/2002/04/052
    12 https://doi.org/10.1016/0550-3213(93)90033-l
    13 https://doi.org/10.1016/s0550-3213(00)00699-4
    14 https://doi.org/10.1016/s0550-3213(01)00062-1
    15 https://doi.org/10.1016/s0550-3213(01)00296-6
    16 https://doi.org/10.1016/s0550-3213(02)00078-0
    17 https://doi.org/10.1016/s0550-3213(02)00762-9
    18 https://doi.org/10.1016/s0550-3213(97)00517-8
    19 https://doi.org/10.1016/s0550-3213(98)00246-6
    20 https://doi.org/10.1016/s0550-3213(99)00646-x
    21 https://doi.org/10.1016/s0550-3213(99)00700-2
    22 https://doi.org/10.4310/atmp.1999.v3.n1.a1
    23 https://doi.org/10.4310/atmp.2000.v4.n4.a1
    24 https://doi.org/10.4310/atmp.2000.v4.n4.a2
    25 schema:datePublished 2002-12-27
    26 schema:datePublishedReg 2002-12-27
    27 schema:description This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.
    28 schema:genre research_article
    29 schema:inLanguage en
    30 schema:isAccessibleForFree true
    31 schema:isPartOf N07587a9b88854cc3b963881ba655a186
    32 Nc281298f47674d1ca51c80045530c25a
    33 sg:journal.1052482
    34 schema:name Symmetries of Toric Duality
    35 schema:pagination 076
    36 schema:productId N95a5d971879f426ab5bd748d5b3020c2
    37 Na8804707093b40ef9ea47718494e176d
    38 Ne90ea1bc25c9441695c307eabae2960d
    39 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031433556
    40 https://doi.org/10.1088/1126-6708/2002/12/076
    41 schema:sdDatePublished 2019-04-10T21:12
    42 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    43 schema:sdPublisher N8a84cfd65db8405d89f54eee4c51a7cc
    44 schema:url http://iopscience.iop.org/article/10.1088/1126-6708/2002/12/076/meta
    45 sgo:license sg:explorer/license/
    46 sgo:sdDataset articles
    47 rdf:type schema:ScholarlyArticle
    48 N07587a9b88854cc3b963881ba655a186 schema:volumeNumber 2002
    49 rdf:type schema:PublicationVolume
    50 N128aceb612ce4bb588692e6f6a4fd8a5 rdf:first sg:person.010540777615.39
    51 rdf:rest rdf:nil
    52 N47bdeb4f64f241c594ad20e15407b0fa rdf:first sg:person.013105053075.99
    53 rdf:rest Ne3794105502846149aaead5bb09e918c
    54 N8a84cfd65db8405d89f54eee4c51a7cc schema:name Springer Nature - SN SciGraph project
    55 rdf:type schema:Organization
    56 N8d00dd77bab640408bc3a5e182d17846 rdf:first sg:person.0614443717.35
    57 rdf:rest N47bdeb4f64f241c594ad20e15407b0fa
    58 N95a5d971879f426ab5bd748d5b3020c2 schema:name doi
    59 schema:value 10.1088/1126-6708/2002/12/076
    60 rdf:type schema:PropertyValue
    61 Na8804707093b40ef9ea47718494e176d schema:name readcube_id
    62 schema:value 95be04cba0edc527f0986ca8fd7e90ff337f4b81624b0742203466ad64cfd6e7
    63 rdf:type schema:PropertyValue
    64 Nc281298f47674d1ca51c80045530c25a schema:issueNumber 12
    65 rdf:type schema:PublicationIssue
    66 Ne3794105502846149aaead5bb09e918c rdf:first sg:person.012155553275.80
    67 rdf:rest N128aceb612ce4bb588692e6f6a4fd8a5
    68 Ne90ea1bc25c9441695c307eabae2960d schema:name dimensions_id
    69 schema:value pub.1031433556
    70 rdf:type schema:PropertyValue
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Pure Mathematics
    76 rdf:type schema:DefinedTerm
    77 sg:journal.1052482 schema:issn 1029-8479
    78 1126-6708
    79 schema:name Journal of High Energy Physics
    80 rdf:type schema:Periodical
    81 sg:person.010540777615.39 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    82 schema:familyName He
    83 schema:givenName Yang-Hui
    84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010540777615.39
    85 rdf:type schema:Person
    86 sg:person.012155553275.80 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    87 schema:familyName Hanany
    88 schema:givenName Amihay
    89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012155553275.80
    90 rdf:type schema:Person
    91 sg:person.013105053075.99 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    92 schema:familyName Franco
    93 schema:givenName Sebastián
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013105053075.99
    95 rdf:type schema:Person
    96 sg:person.0614443717.35 schema:affiliation https://www.grid.ac/institutes/grid.116068.8
    97 schema:familyName Feng
    98 schema:givenName Bo
    99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0614443717.35
    100 rdf:type schema:Person
    101 sg:pub.10.1088/1126-6708/2001/01/018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021289806
    102 https://doi.org/10.1088/1126-6708/2001/01/018
    103 rdf:type schema:CreativeWork
    104 sg:pub.10.1088/1126-6708/2001/02/008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053682608
    105 https://doi.org/10.1088/1126-6708/2001/02/008
    106 rdf:type schema:CreativeWork
    107 sg:pub.10.1088/1126-6708/2001/08/040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008510756
    108 https://doi.org/10.1088/1126-6708/2001/08/040
    109 rdf:type schema:CreativeWork
    110 sg:pub.10.1088/1126-6708/2001/09/008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050733879
    111 https://doi.org/10.1088/1126-6708/2001/09/008
    112 rdf:type schema:CreativeWork
    113 sg:pub.10.1088/1126-6708/2001/12/001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040554299
    114 https://doi.org/10.1088/1126-6708/2001/12/001
    115 rdf:type schema:CreativeWork
    116 sg:pub.10.1088/1126-6708/2001/12/035 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007275558
    117 https://doi.org/10.1088/1126-6708/2001/12/035
    118 rdf:type schema:CreativeWork
    119 sg:pub.10.1088/1126-6708/2002/04/009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023292462
    120 https://doi.org/10.1088/1126-6708/2002/04/009
    121 rdf:type schema:CreativeWork
    122 sg:pub.10.1088/1126-6708/2002/04/052 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003711632
    123 https://doi.org/10.1088/1126-6708/2002/04/052
    124 rdf:type schema:CreativeWork
    125 https://doi.org/10.1016/0550-3213(93)90033-l schema:sameAs https://app.dimensions.ai/details/publication/pub.1004765127
    126 rdf:type schema:CreativeWork
    127 https://doi.org/10.1016/s0550-3213(00)00699-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018210546
    128 rdf:type schema:CreativeWork
    129 https://doi.org/10.1016/s0550-3213(01)00062-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036756880
    130 rdf:type schema:CreativeWork
    131 https://doi.org/10.1016/s0550-3213(01)00296-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027856859
    132 rdf:type schema:CreativeWork
    133 https://doi.org/10.1016/s0550-3213(02)00078-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001677489
    134 rdf:type schema:CreativeWork
    135 https://doi.org/10.1016/s0550-3213(02)00762-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019013456
    136 rdf:type schema:CreativeWork
    137 https://doi.org/10.1016/s0550-3213(97)00517-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016900381
    138 rdf:type schema:CreativeWork
    139 https://doi.org/10.1016/s0550-3213(98)00246-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050310900
    140 rdf:type schema:CreativeWork
    141 https://doi.org/10.1016/s0550-3213(99)00646-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1033701969
    142 rdf:type schema:CreativeWork
    143 https://doi.org/10.1016/s0550-3213(99)00700-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000268900
    144 rdf:type schema:CreativeWork
    145 https://doi.org/10.4310/atmp.1999.v3.n1.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072456932
    146 rdf:type schema:CreativeWork
    147 https://doi.org/10.4310/atmp.2000.v4.n4.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072457001
    148 rdf:type schema:CreativeWork
    149 https://doi.org/10.4310/atmp.2000.v4.n4.a2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072457002
    150 rdf:type schema:CreativeWork
    151 https://www.grid.ac/institutes/grid.116068.8 schema:alternateName Massachusetts Institute of Technology
    152 schema:name Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    153 rdf:type schema:Organization
     




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


    ...