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@ARTICLE{Teschner:169956,
      author       = {Teschner, Jörg and Vartanov, Grigory},
      title        = {6j {S}ymbols for the {M}odular {D}ouble, {Q}uantum
                      {H}yperbolic {G}eometry, and {S}upersymmetric {G}auge
                      {T}heories},
      journal      = {Letters in mathematical physics},
      volume       = {104},
      number       = {5},
      issn         = {1573-0530},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {DESY-2014-02955, DESY-12-035. arXiv:1202.4698},
      pages        = {527 - 551},
      year         = {2014},
      note         = {© Springer Science+Business Media Dordrecht},
      abstract     = {We revisit the definition of the 6j-symbols from the
                      modular double of $U_q(sl(2,R)),$ referred to as b-6j
                      symbols. Our new results are (i) the identification of
                      particularly natural normalization conditions, and (ii) new
                      integral representations for this object. This is used to
                      briefly discuss possible applications to quantum hyperbolic
                      geometry, and to the study of certain supersymmetric gauge
                      theories. We show, in particular, that the b-6j symbol has
                      leading semiclassical asymptotics given by the volume of a
                      non-ideal tetrahedron. We furthermore observe a close
                      relation with the problem to quantize natural Darboux
                      coordinates for moduli spaces of flat connections on Riemann
                      surfaces related to the Fenchel-Nielsen coordinates. Our new
                      integral representations finally indicate a possible
                      interpretation of the b-6j symbols as partition functions of
                      three-dimensional N=2 supersymmetric gauge theories.},
      keywords     = {gauge field theory: supersymmetry (INSPIRE) /
                      supersymmetry: 2 (INSPIRE) / dimension: 3 (INSPIRE) /
                      geometry (INSPIRE) / modular (INSPIRE) / partition function
                      (INSPIRE) / Riemann surface (INSPIRE) / semiclassical
                      (INSPIRE) / quantization (INSPIRE) / moduli space (INSPIRE)
                      / field theory: Liouville (INSPIRE) / approximation:
                      classical (INSPIRE) / n-point function: 4 (INSPIRE) / SU(2)
                      (INSPIRE) / Yang-Mills (INSPIRE) / Chern-Simons term
                      (INSPIRE) / Clebsch-Gordan coefficients (INSPIRE)},
      cin          = {T},
      ddc          = {530},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {51x - Programm Elementarteilchenphysik - Topic unbekannt
                      (POF2-51x)},
      pid          = {G:(DE-HGF)POF2-51x},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000335670100002},
      eprint       = {1202.4698},
      howpublished = {arXiv:1202.4698},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1202.4698;\%\%$},
      doi          = {10.1007/s11005-014-0684-3},
      url          = {https://bib-pubdb1.desy.de/record/169956},
}