@article{8762936,
  abstract     = {{We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with N = 1 supersymmetry. We first calculate the mixed parabolic representation matrix element (or Whittaker function) of U-q(sl(2, R)) and review its applications to Liouville gravity. We then derive the corresponding matrix element for U-q(osp(1 vertical bar 2, R)) and apply it to explain structural features of N = 1 Liouville supergravity. We show that this matrix element has the following properties: (1) its q -> 1 limit is the classical OSp(+)(1 vertical bar 2,R) Whittaker function, (2) it yields the Plancherel measure as the density of black hole states in N = 1 Liouville supergravity, and (3) it leads to 3j-symbols that match with the coupling of boundary vertex operators to the gravitational states as appropriate for N = 1 Liouville supergravity. This object should likewise be of interest in the context of integrability of supersymmetric relativistic Toda chains. We furthermore relate Liouville (super)gravity to dilaton (super)gravity with a hyperbolic sine (pre)potential. We do so by showing that the quantization of the target space Poisson structure in the (graded) Poisson sigma model description leads directly to the quantum group U-q(sl(2, R)) or the quantum supergroup U-q(osp(1 vertical bar 2, R)).}},
  articleno    = {{092}},
  author       = {{Fan, Yale and Mertens, Thomas}},
  issn         = {{1029-8479}},
  journal      = {{JOURNAL OF HIGH ENERGY PHYSICS}},
  keywords     = {{2D Gravity,Models of Quantum Gravity,Quantum Groups,Supergravity Models,GAUGE-THEORY,ASYMPTOTIC SYMMETRIES,REPRESENTATIONS,EIGENFUNCTIONS,SUPERGRAVITY,QUANTIZATION,DEFORMATION,DYNAMICS,OPERATOR,MODELS}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{59}},
  title        = {{From quantum groups to Liouville and dilaton quantum gravity}},
  url          = {{http://doi.org/10.1007/jhep05(2022)092}},
  year         = {{2022}},
}

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