A Unique Connection for Born Geometry View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-08

AUTHORS

Laurent Freidel, Felix J. Rudolph, David Svoboda

ABSTRACT

It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing η and an O(2d) generalized metric H. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing ω. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure (η,ω,H) and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics. More... »

PAGES

1-32

References to SciGraph publications

  • 2010-08. Generalized metric formulation of double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-04-20. T-duality, generalized geometry and non-geometric backgrounds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-11. The effective action of double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2017-11. Generalised kinematics for double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-04. Differential geometry with a projection: application to double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2018-07. Double field theory and membrane sigma-models in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-11. Supergravity as generalised geometry I: type II theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-10. Relative locality: a deepening of the relativity principle in GENERAL RELATIVITY AND GRAVITATION
  • 2015-06. Metastring theory and modular space-time in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-07-30. Doubled geometry and T-folds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-23. Double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-05. On the Riemann tensor in double field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-02. Duality invariant actions and generalised geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-10-21. A geometry for non-geometric string backgrounds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-02. generalised geometry, connections and M theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-21. The gauge algebra of double field theory and Courant brackets in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-12-28. NS-NS fluxes in Hitchin's generalized geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-12. Quantum-Spacetime Phenomenology in LIVING REVIEWS IN RELATIVITY
  • 2014-09. The geometry behind double geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-019-03379-7

    DOI

    http://dx.doi.org/10.1007/s00220-019-03379-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112609204


    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": "Perimeter Institute", 
              "id": "https://www.grid.ac/institutes/grid.420198.6", 
              "name": [
                "Perimeter Institute for Theoretical Physics, 31 Caroline St. N., N2L 2Y5, Waterloo, ON, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Freidel", 
            "givenName": "Laurent", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Ludwig Maximilian University of Munich", 
              "id": "https://www.grid.ac/institutes/grid.5252.0", 
              "name": [
                "Arnold Sommerfeld Center for Theoretical Physics, Department f\u00fcr Physik, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Theresienstr. 37, 80333, Munich, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rudolph", 
            "givenName": "Felix J.", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Perimeter Institute", 
              "id": "https://www.grid.ac/institutes/grid.420198.6", 
              "name": [
                "Perimeter Institute for Theoretical Physics, 31 Caroline St. N., N2L 2Y5, Waterloo, ON, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Svoboda", 
            "givenName": "David", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.12942/lrr-2013-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000707584", 
              "https://doi.org/10.12942/lrr-2013-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-1990-0998124-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002111034"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.4795513", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002784123"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2005.04.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002961729"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2005.04.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002961729"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2015)006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003737877", 
              "https://doi.org/10.1007/jhep06(2015)006"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2015)006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003737877", 
              "https://doi.org/10.1007/jhep06(2015)006"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2012)108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005775932", 
              "https://doi.org/10.1007/jhep02(2012)108"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10714-011-1212-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006541837", 
              "https://doi.org/10.1007/s10714-011-1212-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/12/084", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006582487", 
              "https://doi.org/10.1088/1126-6708/2007/12/084"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2014)070", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007076181", 
              "https://doi.org/10.1007/jhep09(2014)070"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.4848777", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008188736"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0218271815440289", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009028248"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90520-n", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011439271"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90520-n", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011439271"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physletb.2014.01.067", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011674534"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2007.09.021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012104636"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0375-9601(87)90201-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012312490"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0375-9601(87)90201-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012312490"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2014)054", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012882685", 
              "https://doi.org/10.1007/jhep02(2014)054"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015558777", 
              "https://doi.org/10.1088/1126-6708/2009/09/099"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015558777", 
              "https://doi.org/10.1088/1126-6708/2009/09/099"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2009.11.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016173032"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.difgeo.2005.07.002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018020305"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.difgeo.2005.07.002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018020305"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2011)052", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019827619", 
              "https://doi.org/10.1007/jhep11(2011)052"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0218271814420061", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020227988"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1093/qmath/hag025", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020921597"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/30/16/163001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024412528"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2005/10/065", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024677026", 
              "https://doi.org/10.1088/1126-6708/2005/10/065"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2005/10/065", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024677026", 
              "https://doi.org/10.1088/1126-6708/2005/10/065"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1155/ijmms.2005.1737", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025820485"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.3694739", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026087493"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/04/075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028205396", 
              "https://doi.org/10.1088/1126-6708/2009/04/075"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/04/075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028205396", 
              "https://doi.org/10.1088/1126-6708/2009/04/075"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.84.044022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029176314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.84.044022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029176314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(00)00314-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031683209"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2016.12.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032003204"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2016.12.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032003204"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2016.12.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032003204"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep08(2010)008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033009790", 
              "https://doi.org/10.1007/jhep08(2010)008"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep04(2011)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033302262", 
              "https://doi.org/10.1007/jhep04(2011)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.difgeo.2005.06.002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034543012"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.difgeo.2005.06.002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034543012"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2007/07/080", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036255971", 
              "https://doi.org/10.1088/1126-6708/2007/07/080"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/090", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040013290", 
              "https://doi.org/10.1088/1126-6708/2009/09/090"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/090", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040013290", 
              "https://doi.org/10.1088/1126-6708/2009/09/090"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.48.2826", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042389354"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.48.2826", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042389354"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x14500808", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042616463"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2011)091", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042670807", 
              "https://doi.org/10.1007/jhep11(2011)091"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(00)00313-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044763077"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.84.084010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045792608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.84.084010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045792608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(90)91454-j", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047251264"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(90)91454-j", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047251264"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2012)126", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047937064", 
              "https://doi.org/10.1007/jhep05(2012)126"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.47.5453", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053533990"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.47.5453", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053533990"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90266-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054562641"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90266-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054562641"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.92.084053", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060710920"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.92.084053", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060710920"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.45.1057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060785222"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevlett.45.1057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060785222"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1143/ptps.144.145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063142859"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1216/rmjm/1181072105", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064430936"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/jsg.2013.v11.n1.a1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072460833"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/jdg/1214459842", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084460158"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep11(2017)175", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1093045844", 
              "https://doi.org/10.1007/jhep11(2017)175"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/9789813144613_0005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1096103584"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/fic/017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098714844"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep07(2018)015", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1105326951", 
              "https://doi.org/10.1007/jhep07(2018)015"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03-08", 
        "datePublishedReg": "2019-03-08", 
        "description": "It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing \u03b7 and an O(2d) generalized metric H. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing \u03c9. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure (\u03b7,\u03c9,H) and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00220-019-03379-7", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }
        ], 
        "name": "A Unique Connection for Born Geometry", 
        "pagination": "1-32", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "1500f795fc8abe020b205b2e1632ea74334a073e56997afbd01fca949f5f5703"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00220-019-03379-7"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112609204"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00220-019-03379-7", 
          "https://app.dimensions.ai/details/publication/pub.1112609204"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T11:21", 
        "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/v90/0000000354_0000000354/records_11728_00000002.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00220-019-03379-7"
      }
    ]
     

    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/s00220-019-03379-7'

    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/s00220-019-03379-7'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-019-03379-7'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-019-03379-7'


     

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

    250 TRIPLES      21 PREDICATES      78 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00220-019-03379-7 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ne09af25f314d44d19da706a8ecd5e20c
    4 schema:citation sg:pub.10.1007/jhep02(2012)108
    5 sg:pub.10.1007/jhep02(2014)054
    6 sg:pub.10.1007/jhep04(2011)014
    7 sg:pub.10.1007/jhep05(2012)126
    8 sg:pub.10.1007/jhep06(2015)006
    9 sg:pub.10.1007/jhep07(2018)015
    10 sg:pub.10.1007/jhep08(2010)008
    11 sg:pub.10.1007/jhep09(2014)070
    12 sg:pub.10.1007/jhep11(2011)052
    13 sg:pub.10.1007/jhep11(2011)091
    14 sg:pub.10.1007/jhep11(2017)175
    15 sg:pub.10.1007/s10714-011-1212-8
    16 sg:pub.10.1088/1126-6708/2005/10/065
    17 sg:pub.10.1088/1126-6708/2007/07/080
    18 sg:pub.10.1088/1126-6708/2007/12/084
    19 sg:pub.10.1088/1126-6708/2009/04/075
    20 sg:pub.10.1088/1126-6708/2009/09/090
    21 sg:pub.10.1088/1126-6708/2009/09/099
    22 sg:pub.10.12942/lrr-2013-5
    23 https://doi.org/10.1016/0370-2693(90)91454-j
    24 https://doi.org/10.1016/0375-9601(87)90201-5
    25 https://doi.org/10.1016/0550-3213(90)90520-n
    26 https://doi.org/10.1016/0550-3213(91)90266-z
    27 https://doi.org/10.1016/j.difgeo.2005.06.002
    28 https://doi.org/10.1016/j.difgeo.2005.07.002
    29 https://doi.org/10.1016/j.geomphys.2005.04.012
    30 https://doi.org/10.1016/j.geomphys.2016.12.017
    31 https://doi.org/10.1016/j.nuclphysb.2007.09.021
    32 https://doi.org/10.1016/j.nuclphysb.2009.11.001
    33 https://doi.org/10.1016/j.physletb.2014.01.067
    34 https://doi.org/10.1016/s0550-3213(00)00313-8
    35 https://doi.org/10.1016/s0550-3213(00)00314-x
    36 https://doi.org/10.1063/1.3694739
    37 https://doi.org/10.1063/1.4795513
    38 https://doi.org/10.1063/1.4848777
    39 https://doi.org/10.1088/0264-9381/30/16/163001
    40 https://doi.org/10.1090/fic/017
    41 https://doi.org/10.1090/s0002-9947-1990-0998124-1
    42 https://doi.org/10.1093/qmath/hag025
    43 https://doi.org/10.1103/physrevd.47.5453
    44 https://doi.org/10.1103/physrevd.48.2826
    45 https://doi.org/10.1103/physrevd.84.044022
    46 https://doi.org/10.1103/physrevd.84.084010
    47 https://doi.org/10.1103/physrevd.92.084053
    48 https://doi.org/10.1103/physrevlett.45.1057
    49 https://doi.org/10.1142/9789813144613_0005
    50 https://doi.org/10.1142/s0217751x14500808
    51 https://doi.org/10.1142/s0218271814420061
    52 https://doi.org/10.1142/s0218271815440289
    53 https://doi.org/10.1143/ptps.144.145
    54 https://doi.org/10.1155/ijmms.2005.1737
    55 https://doi.org/10.1216/rmjm/1181072105
    56 https://doi.org/10.4310/jdg/1214459842
    57 https://doi.org/10.4310/jsg.2013.v11.n1.a1
    58 schema:datePublished 2019-03-08
    59 schema:datePublishedReg 2019-03-08
    60 schema:description It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing η and an O(2d) generalized metric H. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing ω. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure (η,ω,H) and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.
    61 schema:genre research_article
    62 schema:inLanguage en
    63 schema:isAccessibleForFree false
    64 schema:isPartOf sg:journal.1136216
    65 schema:name A Unique Connection for Born Geometry
    66 schema:pagination 1-32
    67 schema:productId N024aae6124e64fe1881e24e169f10022
    68 N360105f2b822412f82b498dde470f7c2
    69 Na14483a92b3b40608ae49579d1190e2a
    70 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112609204
    71 https://doi.org/10.1007/s00220-019-03379-7
    72 schema:sdDatePublished 2019-04-11T11:21
    73 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    74 schema:sdPublisher N087e66ee4a73401b9ad5a33c7b919fa7
    75 schema:url https://link.springer.com/10.1007%2Fs00220-019-03379-7
    76 sgo:license sg:explorer/license/
    77 sgo:sdDataset articles
    78 rdf:type schema:ScholarlyArticle
    79 N024aae6124e64fe1881e24e169f10022 schema:name dimensions_id
    80 schema:value pub.1112609204
    81 rdf:type schema:PropertyValue
    82 N087e66ee4a73401b9ad5a33c7b919fa7 schema:name Springer Nature - SN SciGraph project
    83 rdf:type schema:Organization
    84 N360105f2b822412f82b498dde470f7c2 schema:name readcube_id
    85 schema:value 1500f795fc8abe020b205b2e1632ea74334a073e56997afbd01fca949f5f5703
    86 rdf:type schema:PropertyValue
    87 N4c5a8cd6b85f41cfac2875b3af0c9a6d rdf:first Nf51d76cf9c184799becab8242287d37e
    88 rdf:rest rdf:nil
    89 N577223585b884f388e250462c1856079 schema:affiliation https://www.grid.ac/institutes/grid.5252.0
    90 schema:familyName Rudolph
    91 schema:givenName Felix J.
    92 rdf:type schema:Person
    93 Na14483a92b3b40608ae49579d1190e2a schema:name doi
    94 schema:value 10.1007/s00220-019-03379-7
    95 rdf:type schema:PropertyValue
    96 Nd207583cda4142989df9f5b034b4ce7d schema:affiliation https://www.grid.ac/institutes/grid.420198.6
    97 schema:familyName Freidel
    98 schema:givenName Laurent
    99 rdf:type schema:Person
    100 Ne09af25f314d44d19da706a8ecd5e20c rdf:first Nd207583cda4142989df9f5b034b4ce7d
    101 rdf:rest Nec5b49a7f90444c8a4e4b6b4d6ef6691
    102 Nec5b49a7f90444c8a4e4b6b4d6ef6691 rdf:first N577223585b884f388e250462c1856079
    103 rdf:rest N4c5a8cd6b85f41cfac2875b3af0c9a6d
    104 Nf51d76cf9c184799becab8242287d37e schema:affiliation https://www.grid.ac/institutes/grid.420198.6
    105 schema:familyName Svoboda
    106 schema:givenName David
    107 rdf:type schema:Person
    108 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    109 schema:name Mathematical Sciences
    110 rdf:type schema:DefinedTerm
    111 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    112 schema:name Pure Mathematics
    113 rdf:type schema:DefinedTerm
    114 sg:journal.1136216 schema:issn 0010-3616
    115 1432-0916
    116 schema:name Communications in Mathematical Physics
    117 rdf:type schema:Periodical
    118 sg:pub.10.1007/jhep02(2012)108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005775932
    119 https://doi.org/10.1007/jhep02(2012)108
    120 rdf:type schema:CreativeWork
    121 sg:pub.10.1007/jhep02(2014)054 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012882685
    122 https://doi.org/10.1007/jhep02(2014)054
    123 rdf:type schema:CreativeWork
    124 sg:pub.10.1007/jhep04(2011)014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033302262
    125 https://doi.org/10.1007/jhep04(2011)014
    126 rdf:type schema:CreativeWork
    127 sg:pub.10.1007/jhep05(2012)126 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047937064
    128 https://doi.org/10.1007/jhep05(2012)126
    129 rdf:type schema:CreativeWork
    130 sg:pub.10.1007/jhep06(2015)006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003737877
    131 https://doi.org/10.1007/jhep06(2015)006
    132 rdf:type schema:CreativeWork
    133 sg:pub.10.1007/jhep07(2018)015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1105326951
    134 https://doi.org/10.1007/jhep07(2018)015
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/jhep08(2010)008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033009790
    137 https://doi.org/10.1007/jhep08(2010)008
    138 rdf:type schema:CreativeWork
    139 sg:pub.10.1007/jhep09(2014)070 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007076181
    140 https://doi.org/10.1007/jhep09(2014)070
    141 rdf:type schema:CreativeWork
    142 sg:pub.10.1007/jhep11(2011)052 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019827619
    143 https://doi.org/10.1007/jhep11(2011)052
    144 rdf:type schema:CreativeWork
    145 sg:pub.10.1007/jhep11(2011)091 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042670807
    146 https://doi.org/10.1007/jhep11(2011)091
    147 rdf:type schema:CreativeWork
    148 sg:pub.10.1007/jhep11(2017)175 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093045844
    149 https://doi.org/10.1007/jhep11(2017)175
    150 rdf:type schema:CreativeWork
    151 sg:pub.10.1007/s10714-011-1212-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006541837
    152 https://doi.org/10.1007/s10714-011-1212-8
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1088/1126-6708/2005/10/065 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024677026
    155 https://doi.org/10.1088/1126-6708/2005/10/065
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1088/1126-6708/2007/07/080 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036255971
    158 https://doi.org/10.1088/1126-6708/2007/07/080
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1088/1126-6708/2007/12/084 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006582487
    161 https://doi.org/10.1088/1126-6708/2007/12/084
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1088/1126-6708/2009/04/075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028205396
    164 https://doi.org/10.1088/1126-6708/2009/04/075
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1088/1126-6708/2009/09/090 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040013290
    167 https://doi.org/10.1088/1126-6708/2009/09/090
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1088/1126-6708/2009/09/099 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015558777
    170 https://doi.org/10.1088/1126-6708/2009/09/099
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.12942/lrr-2013-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000707584
    173 https://doi.org/10.12942/lrr-2013-5
    174 rdf:type schema:CreativeWork
    175 https://doi.org/10.1016/0370-2693(90)91454-j schema:sameAs https://app.dimensions.ai/details/publication/pub.1047251264
    176 rdf:type schema:CreativeWork
    177 https://doi.org/10.1016/0375-9601(87)90201-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012312490
    178 rdf:type schema:CreativeWork
    179 https://doi.org/10.1016/0550-3213(90)90520-n schema:sameAs https://app.dimensions.ai/details/publication/pub.1011439271
    180 rdf:type schema:CreativeWork
    181 https://doi.org/10.1016/0550-3213(91)90266-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1054562641
    182 rdf:type schema:CreativeWork
    183 https://doi.org/10.1016/j.difgeo.2005.06.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034543012
    184 rdf:type schema:CreativeWork
    185 https://doi.org/10.1016/j.difgeo.2005.07.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018020305
    186 rdf:type schema:CreativeWork
    187 https://doi.org/10.1016/j.geomphys.2005.04.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002961729
    188 rdf:type schema:CreativeWork
    189 https://doi.org/10.1016/j.geomphys.2016.12.017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032003204
    190 rdf:type schema:CreativeWork
    191 https://doi.org/10.1016/j.nuclphysb.2007.09.021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012104636
    192 rdf:type schema:CreativeWork
    193 https://doi.org/10.1016/j.nuclphysb.2009.11.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016173032
    194 rdf:type schema:CreativeWork
    195 https://doi.org/10.1016/j.physletb.2014.01.067 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011674534
    196 rdf:type schema:CreativeWork
    197 https://doi.org/10.1016/s0550-3213(00)00313-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044763077
    198 rdf:type schema:CreativeWork
    199 https://doi.org/10.1016/s0550-3213(00)00314-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1031683209
    200 rdf:type schema:CreativeWork
    201 https://doi.org/10.1063/1.3694739 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026087493
    202 rdf:type schema:CreativeWork
    203 https://doi.org/10.1063/1.4795513 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002784123
    204 rdf:type schema:CreativeWork
    205 https://doi.org/10.1063/1.4848777 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008188736
    206 rdf:type schema:CreativeWork
    207 https://doi.org/10.1088/0264-9381/30/16/163001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024412528
    208 rdf:type schema:CreativeWork
    209 https://doi.org/10.1090/fic/017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098714844
    210 rdf:type schema:CreativeWork
    211 https://doi.org/10.1090/s0002-9947-1990-0998124-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002111034
    212 rdf:type schema:CreativeWork
    213 https://doi.org/10.1093/qmath/hag025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020921597
    214 rdf:type schema:CreativeWork
    215 https://doi.org/10.1103/physrevd.47.5453 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053533990
    216 rdf:type schema:CreativeWork
    217 https://doi.org/10.1103/physrevd.48.2826 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042389354
    218 rdf:type schema:CreativeWork
    219 https://doi.org/10.1103/physrevd.84.044022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029176314
    220 rdf:type schema:CreativeWork
    221 https://doi.org/10.1103/physrevd.84.084010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045792608
    222 rdf:type schema:CreativeWork
    223 https://doi.org/10.1103/physrevd.92.084053 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060710920
    224 rdf:type schema:CreativeWork
    225 https://doi.org/10.1103/physrevlett.45.1057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060785222
    226 rdf:type schema:CreativeWork
    227 https://doi.org/10.1142/9789813144613_0005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096103584
    228 rdf:type schema:CreativeWork
    229 https://doi.org/10.1142/s0217751x14500808 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042616463
    230 rdf:type schema:CreativeWork
    231 https://doi.org/10.1142/s0218271814420061 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020227988
    232 rdf:type schema:CreativeWork
    233 https://doi.org/10.1142/s0218271815440289 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009028248
    234 rdf:type schema:CreativeWork
    235 https://doi.org/10.1143/ptps.144.145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063142859
    236 rdf:type schema:CreativeWork
    237 https://doi.org/10.1155/ijmms.2005.1737 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025820485
    238 rdf:type schema:CreativeWork
    239 https://doi.org/10.1216/rmjm/1181072105 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064430936
    240 rdf:type schema:CreativeWork
    241 https://doi.org/10.4310/jdg/1214459842 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084460158
    242 rdf:type schema:CreativeWork
    243 https://doi.org/10.4310/jsg.2013.v11.n1.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072460833
    244 rdf:type schema:CreativeWork
    245 https://www.grid.ac/institutes/grid.420198.6 schema:alternateName Perimeter Institute
    246 schema:name Perimeter Institute for Theoretical Physics, 31 Caroline St. N., N2L 2Y5, Waterloo, ON, Canada
    247 rdf:type schema:Organization
    248 https://www.grid.ac/institutes/grid.5252.0 schema:alternateName Ludwig Maximilian University of Munich
    249 schema:name Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany
    250 rdf:type schema:Organization
     




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


    ...