Analytic continuation of Liouville theory View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-12

AUTHORS

Daniel Harlow, Jonathan Maltz, Edward Witten

ABSTRACT

Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on S2. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville’s equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include “solutions” of Liouville’s equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of “timelike” Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on S2 can be computed by the original Liouville path integral evaluated on a new integration cycle. More... »

PAGES

71

References to SciGraph publications

  • 2010-02. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2010-08. Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models in ANNALES HENRI POINCARÉ
  • 2010-02. Quantum gravity partition functions in three dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 1984-09. Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1999-09. A quantum Teichmüller space in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1987-10. Conformal symmetry in two-dimensional space: Recursion representation of conformal block in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2006-01. Bulk Correlation Functions in 2d Quantum Gravity in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2003-12-01. On minisuperspace models of S-branes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-11-19. Rolling tachyons from Liouville theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-12-03. A conformal field theory for eternal inflation? in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep12(2011)071

    DOI

    http://dx.doi.org/10.1007/jhep12(2011)071

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1012284767


    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": "Stanford University", 
              "id": "https://www.grid.ac/institutes/grid.168010.e", 
              "name": [
                "Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, 94305, Stanford, CA, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Harlow", 
            "givenName": "Daniel", 
            "id": "sg:person.011177163133.11", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011177163133.11"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Stanford University", 
              "id": "https://www.grid.ac/institutes/grid.168010.e", 
              "name": [
                "Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, 94305, Stanford, CA, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Maltz", 
            "givenName": "Jonathan", 
            "id": "sg:person.07577240717.34", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07577240717.34"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institute for Advanced Study", 
              "id": "https://www.grid.ac/institutes/grid.78989.37", 
              "name": [
                "Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, 94305, Stanford, CA, USA", 
                "School of Natural Sciences, Institute for Advanced Study, 08540, Princeton, NJ, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Witten", 
            "givenName": "Edward", 
            "id": "sg:person.016240210261.17", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016240210261.17"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2007.02.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002667012"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1377273", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004058182"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physletb.2003.08.075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007019286"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physletb.2003.08.075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007019286"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01022967", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007098589", 
              "https://doi.org/10.1007/bf01022967"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/18/23/201", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011124727"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(95)01200-a", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014031590"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(99)00071-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015448155"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0370-2693(01)01181-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015783168"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0550-3213(99)00785-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016972109"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.65.104029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017573314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.65.104029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017573314"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)00352-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017792939"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)00352-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017792939"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.80.083531", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019464742"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.80.083531", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019464742"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.65.106006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019729298"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.65.106006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019729298"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2004.03.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019739615"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.74.086003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019980929"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.74.086003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019980929"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1098/rspa.1991.0106", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022538395"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-010-0369-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022882223", 
              "https://doi.org/10.1007/s11005-010-0369-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-010-0369-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022882223", 
              "https://doi.org/10.1007/s11005-010-0369-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01214585", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024987374", 
              "https://doi.org/10.1007/bf01214585"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01214585", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024987374", 
              "https://doi.org/10.1007/bf01214585"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11232-006-0011-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025585468", 
              "https://doi.org/10.1007/s11232-006-0011-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11232-006-0011-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025585468", 
              "https://doi.org/10.1007/s11232-006-0011-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(81)90743-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026584506"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(81)90743-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026584506"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(84)90374-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027639491"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(84)90374-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027639491"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(78)90161-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027753176"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(78)90161-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027753176"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0003-4916(84)90187-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031433830"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/12/019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032320276", 
              "https://doi.org/10.1088/1126-6708/2009/12/019"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/12/019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032320276", 
              "https://doi.org/10.1088/1126-6708/2009/12/019"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2007.01.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032956204"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90510-k", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034155476"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(90)90510-k", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034155476"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035448277", 
              "https://doi.org/10.1007/jhep02(2010)029"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035448277", 
              "https://doi.org/10.1007/jhep02(2010)029"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(84)90052-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035644973"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(84)90052-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035644973"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02557246", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039180460", 
              "https://doi.org/10.1007/bf02557246"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02557246", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039180460", 
              "https://doi.org/10.1007/bf02557246"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2003/11/043", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041634370", 
              "https://doi.org/10.1088/1126-6708/2003/11/043"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(96)00351-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041649759"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00023-010-0044-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042305065", 
              "https://doi.org/10.1007/s00023-010-0044-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00023-010-0044-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042305065", 
              "https://doi.org/10.1007/s00023-010-0044-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2003/12/003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044124825", 
              "https://doi.org/10.1088/1126-6708/2003/12/003"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1098/rspa.1994.0158", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047158279"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/prop.200310109", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048768702"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0003-4916(82)90164-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050446576"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.77.066009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051358505"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.77.066009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051358505"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x04019500", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062923279"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1143/ptps.102.319", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063141834"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.1998.v2.n4.a3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072456914"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.2003.v7.n2.a6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072457086"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2011-12", 
        "datePublishedReg": "2011-12-01", 
        "description": "Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on S2. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville\u2019s equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include \u201csolutions\u201d of Liouville\u2019s equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of \u201ctimelike\u201d Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on S2 can be computed by the original Liouville path integral evaluated on a new integration cycle.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/jhep12(2011)071", 
        "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": "2011"
          }
        ], 
        "name": "Analytic continuation of Liouville theory", 
        "pagination": "71", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "3a876758ded18c670e613ae9379a2c6b7382a478d2b1adf2f952e29b98f050d8"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep12(2011)071"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1012284767"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep12(2011)071", 
          "https://app.dimensions.ai/details/publication/pub.1012284767"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T19:08", 
        "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_8678_00000511.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2FJHEP12%282011%29071"
      }
    ]
     

    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/jhep12(2011)071'

    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/jhep12(2011)071'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep12(2011)071'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep12(2011)071'


     

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

    212 TRIPLES      21 PREDICATES      68 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep12(2011)071 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N4cfd80cd58864d5a9f607e2411d1882f
    4 schema:citation sg:pub.10.1007/bf01022967
    5 sg:pub.10.1007/bf01214585
    6 sg:pub.10.1007/bf02557246
    7 sg:pub.10.1007/jhep02(2010)029
    8 sg:pub.10.1007/s00023-010-0044-5
    9 sg:pub.10.1007/s11005-010-0369-5
    10 sg:pub.10.1007/s11232-006-0011-y
    11 sg:pub.10.1088/1126-6708/2003/11/043
    12 sg:pub.10.1088/1126-6708/2003/12/003
    13 sg:pub.10.1088/1126-6708/2009/12/019
    14 https://doi.org/10.1002/prop.200310109
    15 https://doi.org/10.1016/0003-4916(82)90164-6
    16 https://doi.org/10.1016/0003-4916(84)90187-8
    17 https://doi.org/10.1016/0370-2693(81)90743-7
    18 https://doi.org/10.1016/0370-2693(95)01200-a
    19 https://doi.org/10.1016/0550-3213(78)90161-x
    20 https://doi.org/10.1016/0550-3213(84)90052-x
    21 https://doi.org/10.1016/0550-3213(84)90374-2
    22 https://doi.org/10.1016/0550-3213(90)90510-k
    23 https://doi.org/10.1016/0550-3213(94)00352-1
    24 https://doi.org/10.1016/0550-3213(96)00351-3
    25 https://doi.org/10.1016/j.nuclphysb.2004.03.012
    26 https://doi.org/10.1016/j.nuclphysb.2007.01.008
    27 https://doi.org/10.1016/j.nuclphysb.2007.02.014
    28 https://doi.org/10.1016/j.physletb.2003.08.075
    29 https://doi.org/10.1016/s0370-2693(01)01181-9
    30 https://doi.org/10.1016/s0550-3213(99)00071-1
    31 https://doi.org/10.1016/s0550-3213(99)00785-3
    32 https://doi.org/10.1063/1.1377273
    33 https://doi.org/10.1088/0264-9381/18/23/201
    34 https://doi.org/10.1098/rspa.1991.0106
    35 https://doi.org/10.1098/rspa.1994.0158
    36 https://doi.org/10.1103/physrevd.65.104029
    37 https://doi.org/10.1103/physrevd.65.106006
    38 https://doi.org/10.1103/physrevd.74.086003
    39 https://doi.org/10.1103/physrevd.77.066009
    40 https://doi.org/10.1103/physrevd.80.083531
    41 https://doi.org/10.1142/s0217751x04019500
    42 https://doi.org/10.1143/ptps.102.319
    43 https://doi.org/10.4310/atmp.1998.v2.n4.a3
    44 https://doi.org/10.4310/atmp.2003.v7.n2.a6
    45 schema:datePublished 2011-12
    46 schema:datePublishedReg 2011-12-01
    47 schema:description Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on S2. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville’s equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include “solutions” of Liouville’s equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of “timelike” Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on S2 can be computed by the original Liouville path integral evaluated on a new integration cycle.
    48 schema:genre research_article
    49 schema:inLanguage en
    50 schema:isAccessibleForFree true
    51 schema:isPartOf N8ddd0a55cc90476fada4f7892dd47591
    52 Ndba4600b5eab4d12a8ae4adb2c7de16e
    53 sg:journal.1052482
    54 schema:name Analytic continuation of Liouville theory
    55 schema:pagination 71
    56 schema:productId N10f77e0b71214a10997a785bf4c197bd
    57 N5c37d87687b5448ca0c34f8288899e35
    58 Nf095d41ec79545238aeffc9cd4c1e6bb
    59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012284767
    60 https://doi.org/10.1007/jhep12(2011)071
    61 schema:sdDatePublished 2019-04-10T19:08
    62 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    63 schema:sdPublisher N8e0e6bfbc455446f9726a6ba6666ea18
    64 schema:url http://link.springer.com/10.1007%2FJHEP12%282011%29071
    65 sgo:license sg:explorer/license/
    66 sgo:sdDataset articles
    67 rdf:type schema:ScholarlyArticle
    68 N10f77e0b71214a10997a785bf4c197bd schema:name readcube_id
    69 schema:value 3a876758ded18c670e613ae9379a2c6b7382a478d2b1adf2f952e29b98f050d8
    70 rdf:type schema:PropertyValue
    71 N25a19641240743ce82da99d8ff650095 rdf:first sg:person.07577240717.34
    72 rdf:rest N6ea134402d8941c1ab67dcc34705be0e
    73 N4cfd80cd58864d5a9f607e2411d1882f rdf:first sg:person.011177163133.11
    74 rdf:rest N25a19641240743ce82da99d8ff650095
    75 N5c37d87687b5448ca0c34f8288899e35 schema:name dimensions_id
    76 schema:value pub.1012284767
    77 rdf:type schema:PropertyValue
    78 N6ea134402d8941c1ab67dcc34705be0e rdf:first sg:person.016240210261.17
    79 rdf:rest rdf:nil
    80 N8ddd0a55cc90476fada4f7892dd47591 schema:volumeNumber 2011
    81 rdf:type schema:PublicationVolume
    82 N8e0e6bfbc455446f9726a6ba6666ea18 schema:name Springer Nature - SN SciGraph project
    83 rdf:type schema:Organization
    84 Ndba4600b5eab4d12a8ae4adb2c7de16e schema:issueNumber 12
    85 rdf:type schema:PublicationIssue
    86 Nf095d41ec79545238aeffc9cd4c1e6bb schema:name doi
    87 schema:value 10.1007/jhep12(2011)071
    88 rdf:type schema:PropertyValue
    89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    90 schema:name Mathematical Sciences
    91 rdf:type schema:DefinedTerm
    92 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    93 schema:name Pure Mathematics
    94 rdf:type schema:DefinedTerm
    95 sg:journal.1052482 schema:issn 1029-8479
    96 1126-6708
    97 schema:name Journal of High Energy Physics
    98 rdf:type schema:Periodical
    99 sg:person.011177163133.11 schema:affiliation https://www.grid.ac/institutes/grid.168010.e
    100 schema:familyName Harlow
    101 schema:givenName Daniel
    102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011177163133.11
    103 rdf:type schema:Person
    104 sg:person.016240210261.17 schema:affiliation https://www.grid.ac/institutes/grid.78989.37
    105 schema:familyName Witten
    106 schema:givenName Edward
    107 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016240210261.17
    108 rdf:type schema:Person
    109 sg:person.07577240717.34 schema:affiliation https://www.grid.ac/institutes/grid.168010.e
    110 schema:familyName Maltz
    111 schema:givenName Jonathan
    112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07577240717.34
    113 rdf:type schema:Person
    114 sg:pub.10.1007/bf01022967 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007098589
    115 https://doi.org/10.1007/bf01022967
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/bf01214585 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024987374
    118 https://doi.org/10.1007/bf01214585
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/bf02557246 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039180460
    121 https://doi.org/10.1007/bf02557246
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/jhep02(2010)029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035448277
    124 https://doi.org/10.1007/jhep02(2010)029
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/s00023-010-0044-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042305065
    127 https://doi.org/10.1007/s00023-010-0044-5
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/s11005-010-0369-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022882223
    130 https://doi.org/10.1007/s11005-010-0369-5
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/s11232-006-0011-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1025585468
    133 https://doi.org/10.1007/s11232-006-0011-y
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1088/1126-6708/2003/11/043 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041634370
    136 https://doi.org/10.1088/1126-6708/2003/11/043
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1088/1126-6708/2003/12/003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044124825
    139 https://doi.org/10.1088/1126-6708/2003/12/003
    140 rdf:type schema:CreativeWork
    141 sg:pub.10.1088/1126-6708/2009/12/019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032320276
    142 https://doi.org/10.1088/1126-6708/2009/12/019
    143 rdf:type schema:CreativeWork
    144 https://doi.org/10.1002/prop.200310109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048768702
    145 rdf:type schema:CreativeWork
    146 https://doi.org/10.1016/0003-4916(82)90164-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050446576
    147 rdf:type schema:CreativeWork
    148 https://doi.org/10.1016/0003-4916(84)90187-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031433830
    149 rdf:type schema:CreativeWork
    150 https://doi.org/10.1016/0370-2693(81)90743-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026584506
    151 rdf:type schema:CreativeWork
    152 https://doi.org/10.1016/0370-2693(95)01200-a schema:sameAs https://app.dimensions.ai/details/publication/pub.1014031590
    153 rdf:type schema:CreativeWork
    154 https://doi.org/10.1016/0550-3213(78)90161-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1027753176
    155 rdf:type schema:CreativeWork
    156 https://doi.org/10.1016/0550-3213(84)90052-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1035644973
    157 rdf:type schema:CreativeWork
    158 https://doi.org/10.1016/0550-3213(84)90374-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027639491
    159 rdf:type schema:CreativeWork
    160 https://doi.org/10.1016/0550-3213(90)90510-k schema:sameAs https://app.dimensions.ai/details/publication/pub.1034155476
    161 rdf:type schema:CreativeWork
    162 https://doi.org/10.1016/0550-3213(94)00352-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017792939
    163 rdf:type schema:CreativeWork
    164 https://doi.org/10.1016/0550-3213(96)00351-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041649759
    165 rdf:type schema:CreativeWork
    166 https://doi.org/10.1016/j.nuclphysb.2004.03.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019739615
    167 rdf:type schema:CreativeWork
    168 https://doi.org/10.1016/j.nuclphysb.2007.01.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032956204
    169 rdf:type schema:CreativeWork
    170 https://doi.org/10.1016/j.nuclphysb.2007.02.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002667012
    171 rdf:type schema:CreativeWork
    172 https://doi.org/10.1016/j.physletb.2003.08.075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007019286
    173 rdf:type schema:CreativeWork
    174 https://doi.org/10.1016/s0370-2693(01)01181-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015783168
    175 rdf:type schema:CreativeWork
    176 https://doi.org/10.1016/s0550-3213(99)00071-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015448155
    177 rdf:type schema:CreativeWork
    178 https://doi.org/10.1016/s0550-3213(99)00785-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016972109
    179 rdf:type schema:CreativeWork
    180 https://doi.org/10.1063/1.1377273 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004058182
    181 rdf:type schema:CreativeWork
    182 https://doi.org/10.1088/0264-9381/18/23/201 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011124727
    183 rdf:type schema:CreativeWork
    184 https://doi.org/10.1098/rspa.1991.0106 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022538395
    185 rdf:type schema:CreativeWork
    186 https://doi.org/10.1098/rspa.1994.0158 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047158279
    187 rdf:type schema:CreativeWork
    188 https://doi.org/10.1103/physrevd.65.104029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017573314
    189 rdf:type schema:CreativeWork
    190 https://doi.org/10.1103/physrevd.65.106006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019729298
    191 rdf:type schema:CreativeWork
    192 https://doi.org/10.1103/physrevd.74.086003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019980929
    193 rdf:type schema:CreativeWork
    194 https://doi.org/10.1103/physrevd.77.066009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051358505
    195 rdf:type schema:CreativeWork
    196 https://doi.org/10.1103/physrevd.80.083531 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019464742
    197 rdf:type schema:CreativeWork
    198 https://doi.org/10.1142/s0217751x04019500 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062923279
    199 rdf:type schema:CreativeWork
    200 https://doi.org/10.1143/ptps.102.319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063141834
    201 rdf:type schema:CreativeWork
    202 https://doi.org/10.4310/atmp.1998.v2.n4.a3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072456914
    203 rdf:type schema:CreativeWork
    204 https://doi.org/10.4310/atmp.2003.v7.n2.a6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072457086
    205 rdf:type schema:CreativeWork
    206 https://www.grid.ac/institutes/grid.168010.e schema:alternateName Stanford University
    207 schema:name Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, 94305, Stanford, CA, USA
    208 rdf:type schema:Organization
    209 https://www.grid.ac/institutes/grid.78989.37 schema:alternateName Institute for Advanced Study
    210 schema:name School of Natural Sciences, Institute for Advanced Study, 08540, Princeton, NJ, USA
    211 Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, 94305, Stanford, CA, USA
    212 rdf:type schema:Organization
     




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


    ...