\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\text{SL}}\left( {2,\mathbb{R}} \right) $\end{document} Chern-Simons, Liouville, and gauge theory on ... View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-08

AUTHORS

Yuji Terashima, Masahito Yamazaki

ABSTRACT

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\text{SL}}\left( {2,\mathbb{R}} \right) $\end{document} Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 2 $\end{document} superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmüller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals. More... »

PAGES

135

References to SciGraph publications

  • 1989-09. Quantum field theory and the Jones polynomial in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2008-03-12. Gauging spacetime symmetries on the worldsheet and the geometric Langlands program in JOURNAL OF HIGH ENERGY PHYSICS
  • 1995-07. Discrete Heisenberg-Weyl Group and modular group in LETTERS IN MATHEMATICAL PHYSICS
  • 2009-11-04. AN−1 conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU(N) quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1999-09. A quantum Teichmüller space in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2010-03. S-duality and 2d topological QFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-09-16. Gauging spacetime symmetries on the worldsheet and the geometric Langlands program — II in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-09. Noncommutative Hypergeometry in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-12. Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ)) in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-01-23. Gauge theories from toric geometry and brane tilings in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01. Loop and surface operators in gauge theory and Liouville modular geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-01. Quantization of Teichmüller Spaces and the Quantum Dilogarithm in LETTERS IN MATHEMATICAL PHYSICS
  • 2011-03. Notes on SUSY gauge theories on three-sphere in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-11-19. Bulk-boundary propagator in Liouville theory on a disc in JOURNAL OF HIGH ENERGY PHYSICS
  • 1987-06. The decorated Teichmüller space of punctured surfaces in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2011-05. SUSY gauge theories on squashed three-spheres in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-09. The omega deformation, branes, integrability and Liouville theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 1991-12. Invariants of 3-manifolds via link polynomials and quantum groups in INVENTIONES MATHEMATICAE
  • 1991-03. Quantization of Chern-Simons gauge theory with complex gauge group in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001. The Quantum Dilogarithm and Dehn Twists in Quantum TeichmÜller Theory in INTEGRABLE STRUCTURES OF EXACTLY SOLVABLE TWO-DIMENSIONAL MODELS OF QUANTUM FIELD THEORY
  • 1958-12. On the existence of a connection with curvature zero in COMMENTARII MATHEMATICI HELVETICI
  • 2010-03. Exact results for Wilson loops in superconformal Chern-Simons theories with matter in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-02. Unitary Representations of Uq(??}(2,ℝ)),¶the Modular Double and the Multiparticle q-Deformed¶Toda Chain in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-01-19. Brane dimers and quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2007. Lectures on the Langlands Program and Conformal Field Theory in FRONTIERS IN NUMBER THEORY, PHYSICS, AND GEOMETRY II
  • 1971-12. Bundles with totally disconnected structure group in COMMENTARII MATHEMATICI HELVETICI
  • 1989-11. HeiddenSL(n) symmetry in conformal field theories in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-01. Five-dimensional AGT conjecture and the deformed Virasoro algebra in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02. On AGT conjecture in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-11. Crystal Melting and Toric Calabi-Yau Manifolds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-09-03. Loop operators and S-duality from curves on Riemann surfaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 2001-05. Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-12. AGT on the S-duality wall in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-03. Ground states of S-duality twisted N = 4 super Yang-Mills theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-06. The virtue of defects in 4D gauge theories and 2D CFTs in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-08. A uniqueness property for the quantization of Teichmüller Spaces in GEOMETRIAE DEDICATA
  • 2010-02. Gauge theory loop operators and Liouville theory in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep08(2011)135

    DOI

    http://dx.doi.org/10.1007/jhep08(2011)135

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046909813


    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": "Tokyo Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.32197.3e", 
              "name": [
                "Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8551, Tokyo, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Terashima", 
            "givenName": "Yuji", 
            "id": "sg:person.012013047275.16", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012013047275.16"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Princeton University", 
              "id": "https://www.grid.ac/institutes/grid.16750.35", 
              "name": [
                "Princeton Center for Theoretical Science, Princeton University, 08544, Princeton, NJ, U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yamazaki", 
            "givenName": "Masahito", 
            "id": "sg:person.012735326423.30", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012735326423.30"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/0550-3213(88)90143-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000125557"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(88)90143-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000125557"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200100592", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001823396", 
              "https://doi.org/10.1007/s002200100592"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0370-2693(89)80025-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002956260"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1342-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003420438", 
              "https://doi.org/10.1007/s00220-005-1342-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1342-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003420438", 
              "https://doi.org/10.1007/s00220-005-1342-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1342-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003420438", 
              "https://doi.org/10.1007/s00220-005-1342-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep05(2011)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003742519", 
              "https://doi.org/10.1007/jhep05(2011)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(89)90436-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003878513"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(89)90436-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003878513"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0920-5632(97)00306-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004224905"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-010-0670-5_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004883364", 
              "https://doi.org/10.1007/978-94-010-0670-5_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(93)91618-w", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005551512"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(93)91618-w", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005551512"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/01/128", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006061897", 
              "https://doi.org/10.1088/1126-6708/2006/01/128"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/01/128", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006061897", 
              "https://doi.org/10.1088/1126-6708/2006/01/128"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02566843", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007711021", 
              "https://doi.org/10.1007/bf02566843"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physletb.2010.06.027", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007731577"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep09(2010)092", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007800644", 
              "https://doi.org/10.1007/jhep09(2010)092"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/12/12/012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009626290"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2011)127", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010940528", 
              "https://doi.org/10.1007/jhep03(2011)127"
            ], 
            "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": "sg:pub.10.1007/s002200100412", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015556503", 
              "https://doi.org/10.1007/s002200100412"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(92)90188-h", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015622852"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(92)90188-h", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015622852"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02564579", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016809678", 
              "https://doi.org/10.1007/bf02564579"
            ], 
            "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": "sg:pub.10.1007/jhep03(2011)099", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018431428", 
              "https://doi.org/10.1007/jhep03(2011)099"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.83.066007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019477464"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.83.066007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019477464"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1007460128279", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020216318", 
              "https://doi.org/10.1023/a:1007460128279"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(89)90130-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022212793"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(89)90130-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022212793"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep12(2010)079", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022546572", 
              "https://doi.org/10.1007/jhep12(2010)079"
            ], 
            "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": "https://doi.org/10.1103/physrevd.63.126001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024221658"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrevd.63.126001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024221658"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0040-9383(92)90044-i", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025284675"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025314613", 
              "https://doi.org/10.1007/jhep03(2010)032"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025314613", 
              "https://doi.org/10.1007/jhep03(2010)032"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysbps.2011.04.150", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026708150"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0166-8641(82)90035-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026723628"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026825461", 
              "https://doi.org/10.1007/jhep02(2010)057"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026825461", 
              "https://doi.org/10.1007/jhep02(2010)057"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0040-9383(92)90016-b", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027892611"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0040-9383(92)90015-a", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028642877"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01872779", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028671073", 
              "https://doi.org/10.1007/bf01872779"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.geomphys.2007.03.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029124475"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01217730", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033035951", 
              "https://doi.org/10.1007/bf01217730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01217730", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033035951", 
              "https://doi.org/10.1007/bf01217730"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep06(2011)025", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033726360", 
              "https://doi.org/10.1007/jhep06(2011)025"
            ], 
            "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": "https://doi.org/10.1016/j.physletb.2009.10.077", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035872804"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/11/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036176184", 
              "https://doi.org/10.1088/1126-6708/2009/11/002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/11/002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036176184", 
              "https://doi.org/10.1088/1126-6708/2009/11/002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/35/18/304", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038001324"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00005590", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038246031", 
              "https://doi.org/10.1007/pl00005590"
            ], 
            "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.10.1007/bf02124331", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040269024", 
              "https://doi.org/10.1007/bf02124331"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02124331", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040269024", 
              "https://doi.org/10.1007/bf02124331"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2008/09/074", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040903808", 
              "https://doi.org/10.1088/1126-6708/2008/09/074"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099116", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040916816", 
              "https://doi.org/10.1007/bf02099116"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099116", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040916816", 
              "https://doi.org/10.1007/bf02099116"
            ], 
            "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.10.1088/1126-6708/2006/01/096", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042410190", 
              "https://doi.org/10.1088/1126-6708/2006/01/096"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2006/01/096", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042410190", 
              "https://doi.org/10.1088/1126-6708/2006/01/096"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.physletb.2010.01.036", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043434953"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90558-f", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043973672"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(91)90558-f", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043973672"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2011.03.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046389669"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046823399", 
              "https://doi.org/10.1007/jhep02(2010)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep02(2010)014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046823399", 
              "https://doi.org/10.1007/jhep02(2010)014"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-009-0836-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046921720", 
              "https://doi.org/10.1007/s00220-009-0836-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-009-0836-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046921720", 
              "https://doi.org/10.1007/s00220-009-0836-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-009-0836-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046921720", 
              "https://doi.org/10.1007/s00220-009-0836-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01223515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047039592", 
              "https://doi.org/10.1007/bf01223515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01223515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047039592", 
              "https://doi.org/10.1007/bf01223515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/plms/s3-55.1.59", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048378410"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2001/11/044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049569486", 
              "https://doi.org/10.1088/1126-6708/2001/11/044"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(96)01088-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049623391"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)125", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049735189", 
              "https://doi.org/10.1007/jhep01(2010)125"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)125", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049735189", 
              "https://doi.org/10.1007/jhep01(2010)125"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051074521", 
              "https://doi.org/10.1007/jhep01(2010)113"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep01(2010)113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051074521", 
              "https://doi.org/10.1007/jhep01(2010)113"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-30308-4_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051139032", 
              "https://doi.org/10.1007/978-3-540-30308-4_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(88)90603-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051170725"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(88)90603-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051170725"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10711-007-9176-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052005489", 
              "https://doi.org/10.1007/s10711-007-9176-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)089", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052358077", 
              "https://doi.org/10.1007/jhep03(2010)089"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/jhep03(2010)089", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052358077", 
              "https://doi.org/10.1007/jhep03(2010)089"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nuclphysb.2009.09.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052940666"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053003276", 
              "https://doi.org/10.1088/1126-6708/2009/09/031"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2009/09/031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053003276", 
              "https://doi.org/10.1088/1126-6708/2009/09/031"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01239527", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053649616", 
              "https://doi.org/10.1007/bf01239527"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.531809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058108381"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2008/03/033", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059132730", 
              "https://doi.org/10.1088/1126-6708/2008/03/033"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217732387001130", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062917196"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217732394000447", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062919390"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217732394003610", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062919707"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x0100444x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062921807"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x04020567", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062923370"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x09044607", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062925764"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1143/ptp.124.227", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063129547"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/agt.2009.9.1791", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069057848"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/gt.2008.12.1171", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069060158"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/2007075", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069694836"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/atmp.2003.v7.n5.a4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072457101"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/cntp.2009.v3.n2.a4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072459465"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/9789814434461_0014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1088772265"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2011-08", 
        "datePublishedReg": "2011-08-01", 
        "description": "We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$ {\\text{SL}}\\left( {2,\\mathbb{R}} \\right) $\\end{document} Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$ \\mathcal{N} = 2 $\\end{document} superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichm\u00fcller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/jhep08(2011)135", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "8", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2011"
          }
        ], 
        "name": "\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$ {\\text{SL}}\\left( {2,\\mathbb{R}} \\right) $\\end{document} Chern-Simons, Liouville, and gauge theory on duality walls", 
        "pagination": "135", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "df75fd996df4a1dcc7e1e0bb9f7f6da586c2733d5b94295695d5f272cdf807c4"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/jhep08(2011)135"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1046909813"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/jhep08(2011)135", 
          "https://app.dimensions.ai/details/publication/pub.1046909813"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T13:18", 
        "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_8659_00000515.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2FJHEP08%282011%29135"
      }
    ]
     

    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/jhep08(2011)135'

    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/jhep08(2011)135'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/jhep08(2011)135'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/jhep08(2011)135'


     

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

    355 TRIPLES      21 PREDICATES      109 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/jhep08(2011)135 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N862dcc880eba4842a776c030acfcd424
    4 schema:citation sg:pub.10.1007/978-3-540-30308-4_11
    5 sg:pub.10.1007/978-94-010-0670-5_13
    6 sg:pub.10.1007/bf01217730
    7 sg:pub.10.1007/bf01223515
    8 sg:pub.10.1007/bf01239527
    9 sg:pub.10.1007/bf01872779
    10 sg:pub.10.1007/bf02099116
    11 sg:pub.10.1007/bf02124331
    12 sg:pub.10.1007/bf02557246
    13 sg:pub.10.1007/bf02564579
    14 sg:pub.10.1007/bf02566843
    15 sg:pub.10.1007/jhep01(2010)113
    16 sg:pub.10.1007/jhep01(2010)125
    17 sg:pub.10.1007/jhep02(2010)014
    18 sg:pub.10.1007/jhep02(2010)057
    19 sg:pub.10.1007/jhep03(2010)032
    20 sg:pub.10.1007/jhep03(2010)089
    21 sg:pub.10.1007/jhep03(2011)099
    22 sg:pub.10.1007/jhep03(2011)127
    23 sg:pub.10.1007/jhep05(2011)014
    24 sg:pub.10.1007/jhep06(2011)025
    25 sg:pub.10.1007/jhep09(2010)092
    26 sg:pub.10.1007/jhep12(2010)079
    27 sg:pub.10.1007/pl00005590
    28 sg:pub.10.1007/s00220-005-1342-5
    29 sg:pub.10.1007/s00220-009-0836-y
    30 sg:pub.10.1007/s002200100412
    31 sg:pub.10.1007/s002200100592
    32 sg:pub.10.1007/s10711-007-9176-2
    33 sg:pub.10.1007/s11005-010-0369-5
    34 sg:pub.10.1023/a:1007460128279
    35 sg:pub.10.1088/1126-6708/2001/11/044
    36 sg:pub.10.1088/1126-6708/2006/01/096
    37 sg:pub.10.1088/1126-6708/2006/01/128
    38 sg:pub.10.1088/1126-6708/2008/03/033
    39 sg:pub.10.1088/1126-6708/2008/09/074
    40 sg:pub.10.1088/1126-6708/2009/09/031
    41 sg:pub.10.1088/1126-6708/2009/11/002
    42 https://doi.org/10.1016/0040-9383(92)90015-a
    43 https://doi.org/10.1016/0040-9383(92)90016-b
    44 https://doi.org/10.1016/0040-9383(92)90044-i
    45 https://doi.org/10.1016/0166-8641(82)90035-9
    46 https://doi.org/10.1016/0370-2693(93)91618-w
    47 https://doi.org/10.1016/0370-2693(96)01088-x
    48 https://doi.org/10.1016/0550-3213(88)90143-5
    49 https://doi.org/10.1016/0550-3213(88)90603-7
    50 https://doi.org/10.1016/0550-3213(89)90130-2
    51 https://doi.org/10.1016/0550-3213(89)90436-7
    52 https://doi.org/10.1016/0550-3213(90)90510-k
    53 https://doi.org/10.1016/0550-3213(91)90558-f
    54 https://doi.org/10.1016/0550-3213(92)90188-h
    55 https://doi.org/10.1016/0550-3213(94)00352-1
    56 https://doi.org/10.1016/0550-3213(96)00351-3
    57 https://doi.org/10.1016/j.geomphys.2007.03.008
    58 https://doi.org/10.1016/j.nuclphysb.2009.09.011
    59 https://doi.org/10.1016/j.nuclphysb.2011.03.014
    60 https://doi.org/10.1016/j.nuclphysbps.2011.04.150
    61 https://doi.org/10.1016/j.physletb.2009.10.077
    62 https://doi.org/10.1016/j.physletb.2010.01.036
    63 https://doi.org/10.1016/j.physletb.2010.06.027
    64 https://doi.org/10.1016/s0370-2693(89)80025-5
    65 https://doi.org/10.1016/s0920-5632(97)00306-x
    66 https://doi.org/10.1063/1.531809
    67 https://doi.org/10.1088/0264-9381/12/12/012
    68 https://doi.org/10.1088/0264-9381/18/23/201
    69 https://doi.org/10.1088/0305-4470/35/18/304
    70 https://doi.org/10.1103/physrevd.63.126001
    71 https://doi.org/10.1103/physrevd.83.066007
    72 https://doi.org/10.1112/plms/s3-55.1.59
    73 https://doi.org/10.1142/9789814434461_0014
    74 https://doi.org/10.1142/s0217732387001130
    75 https://doi.org/10.1142/s0217732394000447
    76 https://doi.org/10.1142/s0217732394003610
    77 https://doi.org/10.1142/s0217751x0100444x
    78 https://doi.org/10.1142/s0217751x04020567
    79 https://doi.org/10.1142/s0217751x09044607
    80 https://doi.org/10.1143/ptp.124.227
    81 https://doi.org/10.2140/agt.2009.9.1791
    82 https://doi.org/10.2140/gt.2008.12.1171
    83 https://doi.org/10.2307/2007075
    84 https://doi.org/10.4310/atmp.2003.v7.n5.a4
    85 https://doi.org/10.4310/cntp.2009.v3.n2.a4
    86 schema:datePublished 2011-08
    87 schema:datePublishedReg 2011-08-01
    88 schema:description We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\text{SL}}\left( {2,\mathbb{R}} \right) $\end{document} Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 2 $\end{document} superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmüller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.
    89 schema:genre research_article
    90 schema:inLanguage en
    91 schema:isAccessibleForFree true
    92 schema:isPartOf Nad8da8b4aa544c42ad95c2abfe2dd2d7
    93 Ne6b5681e2d3f42f0a90747738f83763b
    94 sg:journal.1052482
    95 schema:name \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\text{SL}}\left( {2,\mathbb{R}} \right) $\end{document} Chern-Simons, Liouville, and gauge theory on duality walls
    96 schema:pagination 135
    97 schema:productId N3a94b7d8d85f47b0bcf3d2c53e83d961
    98 N55b1b60aa195465fa17df69c303770c2
    99 N7bb7851db2c9429bbf31508229daf0d1
    100 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046909813
    101 https://doi.org/10.1007/jhep08(2011)135
    102 schema:sdDatePublished 2019-04-10T13:18
    103 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    104 schema:sdPublisher Na84b68e55ba64679933803c2637e6a3a
    105 schema:url http://link.springer.com/10.1007%2FJHEP08%282011%29135
    106 sgo:license sg:explorer/license/
    107 sgo:sdDataset articles
    108 rdf:type schema:ScholarlyArticle
    109 N3a94b7d8d85f47b0bcf3d2c53e83d961 schema:name dimensions_id
    110 schema:value pub.1046909813
    111 rdf:type schema:PropertyValue
    112 N55b1b60aa195465fa17df69c303770c2 schema:name readcube_id
    113 schema:value df75fd996df4a1dcc7e1e0bb9f7f6da586c2733d5b94295695d5f272cdf807c4
    114 rdf:type schema:PropertyValue
    115 N7bb7851db2c9429bbf31508229daf0d1 schema:name doi
    116 schema:value 10.1007/jhep08(2011)135
    117 rdf:type schema:PropertyValue
    118 N862dcc880eba4842a776c030acfcd424 rdf:first sg:person.012013047275.16
    119 rdf:rest N88e2673cab474925884cdc895d76f79e
    120 N88e2673cab474925884cdc895d76f79e rdf:first sg:person.012735326423.30
    121 rdf:rest rdf:nil
    122 Na84b68e55ba64679933803c2637e6a3a schema:name Springer Nature - SN SciGraph project
    123 rdf:type schema:Organization
    124 Nad8da8b4aa544c42ad95c2abfe2dd2d7 schema:volumeNumber 2011
    125 rdf:type schema:PublicationVolume
    126 Ne6b5681e2d3f42f0a90747738f83763b schema:issueNumber 8
    127 rdf:type schema:PublicationIssue
    128 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    129 schema:name Mathematical Sciences
    130 rdf:type schema:DefinedTerm
    131 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    132 schema:name Pure Mathematics
    133 rdf:type schema:DefinedTerm
    134 sg:journal.1052482 schema:issn 1029-8479
    135 1126-6708
    136 schema:name Journal of High Energy Physics
    137 rdf:type schema:Periodical
    138 sg:person.012013047275.16 schema:affiliation https://www.grid.ac/institutes/grid.32197.3e
    139 schema:familyName Terashima
    140 schema:givenName Yuji
    141 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012013047275.16
    142 rdf:type schema:Person
    143 sg:person.012735326423.30 schema:affiliation https://www.grid.ac/institutes/grid.16750.35
    144 schema:familyName Yamazaki
    145 schema:givenName Masahito
    146 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012735326423.30
    147 rdf:type schema:Person
    148 sg:pub.10.1007/978-3-540-30308-4_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051139032
    149 https://doi.org/10.1007/978-3-540-30308-4_11
    150 rdf:type schema:CreativeWork
    151 sg:pub.10.1007/978-94-010-0670-5_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004883364
    152 https://doi.org/10.1007/978-94-010-0670-5_13
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1007/bf01217730 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033035951
    155 https://doi.org/10.1007/bf01217730
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/bf01223515 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047039592
    158 https://doi.org/10.1007/bf01223515
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/bf01239527 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053649616
    161 https://doi.org/10.1007/bf01239527
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1007/bf01872779 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028671073
    164 https://doi.org/10.1007/bf01872779
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1007/bf02099116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040916816
    167 https://doi.org/10.1007/bf02099116
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/bf02124331 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040269024
    170 https://doi.org/10.1007/bf02124331
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/bf02557246 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039180460
    173 https://doi.org/10.1007/bf02557246
    174 rdf:type schema:CreativeWork
    175 sg:pub.10.1007/bf02564579 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016809678
    176 https://doi.org/10.1007/bf02564579
    177 rdf:type schema:CreativeWork
    178 sg:pub.10.1007/bf02566843 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007711021
    179 https://doi.org/10.1007/bf02566843
    180 rdf:type schema:CreativeWork
    181 sg:pub.10.1007/jhep01(2010)113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051074521
    182 https://doi.org/10.1007/jhep01(2010)113
    183 rdf:type schema:CreativeWork
    184 sg:pub.10.1007/jhep01(2010)125 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049735189
    185 https://doi.org/10.1007/jhep01(2010)125
    186 rdf:type schema:CreativeWork
    187 sg:pub.10.1007/jhep02(2010)014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046823399
    188 https://doi.org/10.1007/jhep02(2010)014
    189 rdf:type schema:CreativeWork
    190 sg:pub.10.1007/jhep02(2010)057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026825461
    191 https://doi.org/10.1007/jhep02(2010)057
    192 rdf:type schema:CreativeWork
    193 sg:pub.10.1007/jhep03(2010)032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025314613
    194 https://doi.org/10.1007/jhep03(2010)032
    195 rdf:type schema:CreativeWork
    196 sg:pub.10.1007/jhep03(2010)089 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052358077
    197 https://doi.org/10.1007/jhep03(2010)089
    198 rdf:type schema:CreativeWork
    199 sg:pub.10.1007/jhep03(2011)099 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018431428
    200 https://doi.org/10.1007/jhep03(2011)099
    201 rdf:type schema:CreativeWork
    202 sg:pub.10.1007/jhep03(2011)127 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010940528
    203 https://doi.org/10.1007/jhep03(2011)127
    204 rdf:type schema:CreativeWork
    205 sg:pub.10.1007/jhep05(2011)014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003742519
    206 https://doi.org/10.1007/jhep05(2011)014
    207 rdf:type schema:CreativeWork
    208 sg:pub.10.1007/jhep06(2011)025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033726360
    209 https://doi.org/10.1007/jhep06(2011)025
    210 rdf:type schema:CreativeWork
    211 sg:pub.10.1007/jhep09(2010)092 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007800644
    212 https://doi.org/10.1007/jhep09(2010)092
    213 rdf:type schema:CreativeWork
    214 sg:pub.10.1007/jhep12(2010)079 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022546572
    215 https://doi.org/10.1007/jhep12(2010)079
    216 rdf:type schema:CreativeWork
    217 sg:pub.10.1007/pl00005590 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038246031
    218 https://doi.org/10.1007/pl00005590
    219 rdf:type schema:CreativeWork
    220 sg:pub.10.1007/s00220-005-1342-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003420438
    221 https://doi.org/10.1007/s00220-005-1342-5
    222 rdf:type schema:CreativeWork
    223 sg:pub.10.1007/s00220-009-0836-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1046921720
    224 https://doi.org/10.1007/s00220-009-0836-y
    225 rdf:type schema:CreativeWork
    226 sg:pub.10.1007/s002200100412 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015556503
    227 https://doi.org/10.1007/s002200100412
    228 rdf:type schema:CreativeWork
    229 sg:pub.10.1007/s002200100592 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001823396
    230 https://doi.org/10.1007/s002200100592
    231 rdf:type schema:CreativeWork
    232 sg:pub.10.1007/s10711-007-9176-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052005489
    233 https://doi.org/10.1007/s10711-007-9176-2
    234 rdf:type schema:CreativeWork
    235 sg:pub.10.1007/s11005-010-0369-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022882223
    236 https://doi.org/10.1007/s11005-010-0369-5
    237 rdf:type schema:CreativeWork
    238 sg:pub.10.1023/a:1007460128279 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020216318
    239 https://doi.org/10.1023/a:1007460128279
    240 rdf:type schema:CreativeWork
    241 sg:pub.10.1088/1126-6708/2001/11/044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049569486
    242 https://doi.org/10.1088/1126-6708/2001/11/044
    243 rdf:type schema:CreativeWork
    244 sg:pub.10.1088/1126-6708/2006/01/096 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042410190
    245 https://doi.org/10.1088/1126-6708/2006/01/096
    246 rdf:type schema:CreativeWork
    247 sg:pub.10.1088/1126-6708/2006/01/128 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006061897
    248 https://doi.org/10.1088/1126-6708/2006/01/128
    249 rdf:type schema:CreativeWork
    250 sg:pub.10.1088/1126-6708/2008/03/033 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059132730
    251 https://doi.org/10.1088/1126-6708/2008/03/033
    252 rdf:type schema:CreativeWork
    253 sg:pub.10.1088/1126-6708/2008/09/074 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040903808
    254 https://doi.org/10.1088/1126-6708/2008/09/074
    255 rdf:type schema:CreativeWork
    256 sg:pub.10.1088/1126-6708/2009/09/031 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053003276
    257 https://doi.org/10.1088/1126-6708/2009/09/031
    258 rdf:type schema:CreativeWork
    259 sg:pub.10.1088/1126-6708/2009/11/002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036176184
    260 https://doi.org/10.1088/1126-6708/2009/11/002
    261 rdf:type schema:CreativeWork
    262 https://doi.org/10.1016/0040-9383(92)90015-a schema:sameAs https://app.dimensions.ai/details/publication/pub.1028642877
    263 rdf:type schema:CreativeWork
    264 https://doi.org/10.1016/0040-9383(92)90016-b schema:sameAs https://app.dimensions.ai/details/publication/pub.1027892611
    265 rdf:type schema:CreativeWork
    266 https://doi.org/10.1016/0040-9383(92)90044-i schema:sameAs https://app.dimensions.ai/details/publication/pub.1025284675
    267 rdf:type schema:CreativeWork
    268 https://doi.org/10.1016/0166-8641(82)90035-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026723628
    269 rdf:type schema:CreativeWork
    270 https://doi.org/10.1016/0370-2693(93)91618-w schema:sameAs https://app.dimensions.ai/details/publication/pub.1005551512
    271 rdf:type schema:CreativeWork
    272 https://doi.org/10.1016/0370-2693(96)01088-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1049623391
    273 rdf:type schema:CreativeWork
    274 https://doi.org/10.1016/0550-3213(88)90143-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000125557
    275 rdf:type schema:CreativeWork
    276 https://doi.org/10.1016/0550-3213(88)90603-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051170725
    277 rdf:type schema:CreativeWork
    278 https://doi.org/10.1016/0550-3213(89)90130-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022212793
    279 rdf:type schema:CreativeWork
    280 https://doi.org/10.1016/0550-3213(89)90436-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003878513
    281 rdf:type schema:CreativeWork
    282 https://doi.org/10.1016/0550-3213(90)90510-k schema:sameAs https://app.dimensions.ai/details/publication/pub.1034155476
    283 rdf:type schema:CreativeWork
    284 https://doi.org/10.1016/0550-3213(91)90558-f schema:sameAs https://app.dimensions.ai/details/publication/pub.1043973672
    285 rdf:type schema:CreativeWork
    286 https://doi.org/10.1016/0550-3213(92)90188-h schema:sameAs https://app.dimensions.ai/details/publication/pub.1015622852
    287 rdf:type schema:CreativeWork
    288 https://doi.org/10.1016/0550-3213(94)00352-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017792939
    289 rdf:type schema:CreativeWork
    290 https://doi.org/10.1016/0550-3213(96)00351-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041649759
    291 rdf:type schema:CreativeWork
    292 https://doi.org/10.1016/j.geomphys.2007.03.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029124475
    293 rdf:type schema:CreativeWork
    294 https://doi.org/10.1016/j.nuclphysb.2009.09.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052940666
    295 rdf:type schema:CreativeWork
    296 https://doi.org/10.1016/j.nuclphysb.2011.03.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046389669
    297 rdf:type schema:CreativeWork
    298 https://doi.org/10.1016/j.nuclphysbps.2011.04.150 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026708150
    299 rdf:type schema:CreativeWork
    300 https://doi.org/10.1016/j.physletb.2009.10.077 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035872804
    301 rdf:type schema:CreativeWork
    302 https://doi.org/10.1016/j.physletb.2010.01.036 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043434953
    303 rdf:type schema:CreativeWork
    304 https://doi.org/10.1016/j.physletb.2010.06.027 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007731577
    305 rdf:type schema:CreativeWork
    306 https://doi.org/10.1016/s0370-2693(89)80025-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002956260
    307 rdf:type schema:CreativeWork
    308 https://doi.org/10.1016/s0920-5632(97)00306-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1004224905
    309 rdf:type schema:CreativeWork
    310 https://doi.org/10.1063/1.531809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058108381
    311 rdf:type schema:CreativeWork
    312 https://doi.org/10.1088/0264-9381/12/12/012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009626290
    313 rdf:type schema:CreativeWork
    314 https://doi.org/10.1088/0264-9381/18/23/201 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011124727
    315 rdf:type schema:CreativeWork
    316 https://doi.org/10.1088/0305-4470/35/18/304 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038001324
    317 rdf:type schema:CreativeWork
    318 https://doi.org/10.1103/physrevd.63.126001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024221658
    319 rdf:type schema:CreativeWork
    320 https://doi.org/10.1103/physrevd.83.066007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019477464
    321 rdf:type schema:CreativeWork
    322 https://doi.org/10.1112/plms/s3-55.1.59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048378410
    323 rdf:type schema:CreativeWork
    324 https://doi.org/10.1142/9789814434461_0014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1088772265
    325 rdf:type schema:CreativeWork
    326 https://doi.org/10.1142/s0217732387001130 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062917196
    327 rdf:type schema:CreativeWork
    328 https://doi.org/10.1142/s0217732394000447 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062919390
    329 rdf:type schema:CreativeWork
    330 https://doi.org/10.1142/s0217732394003610 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062919707
    331 rdf:type schema:CreativeWork
    332 https://doi.org/10.1142/s0217751x0100444x schema:sameAs https://app.dimensions.ai/details/publication/pub.1062921807
    333 rdf:type schema:CreativeWork
    334 https://doi.org/10.1142/s0217751x04020567 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062923370
    335 rdf:type schema:CreativeWork
    336 https://doi.org/10.1142/s0217751x09044607 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062925764
    337 rdf:type schema:CreativeWork
    338 https://doi.org/10.1143/ptp.124.227 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063129547
    339 rdf:type schema:CreativeWork
    340 https://doi.org/10.2140/agt.2009.9.1791 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069057848
    341 rdf:type schema:CreativeWork
    342 https://doi.org/10.2140/gt.2008.12.1171 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069060158
    343 rdf:type schema:CreativeWork
    344 https://doi.org/10.2307/2007075 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069694836
    345 rdf:type schema:CreativeWork
    346 https://doi.org/10.4310/atmp.2003.v7.n5.a4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072457101
    347 rdf:type schema:CreativeWork
    348 https://doi.org/10.4310/cntp.2009.v3.n2.a4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072459465
    349 rdf:type schema:CreativeWork
    350 https://www.grid.ac/institutes/grid.16750.35 schema:alternateName Princeton University
    351 schema:name Princeton Center for Theoretical Science, Princeton University, 08544, Princeton, NJ, U.S.A.
    352 rdf:type schema:Organization
    353 https://www.grid.ac/institutes/grid.32197.3e schema:alternateName Tokyo Institute of Technology
    354 schema:name Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8551, Tokyo, Japan
    355 rdf:type schema:Organization
     




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


    ...